Logo
Unionpedia
Communication
Get it on Google Play
New! Download Unionpedia on your Android™ device!
Download
Faster access than browser!
 

Bernoulli number

Index Bernoulli number

In mathematics, the Bernoulli numbers are a sequence of rational numbers which occur frequently in number theory. [1]

129 relations: Abraham de Moivre, Ada Lovelace, Agoh–Giuga conjecture, Al-Karaji, Algebraic number, Algorithm, Alternating permutation, Analytical Engine, Ankeny–Artin–Chowla congruence, Antiderivative, Archimedes, Ars Conjectandi, Aryabhata, Asymptotic analysis, Asymptotic expansion, Bernoulli polynomials, Big O notation, Binomial coefficient, Blaise Pascal, Boustrophedon transform, Carl Gustav Jacob Jacobi, Charles Babbage, Chinese remainder theorem, Closed manifold, Closed-form expression, Coefficient, Computational complexity theory, Computer program, Converse relation, Cumulant, Cyclotomic field, Désiré André, Differentiable manifold, Digamma function, Dimension, Dirichlet character, Dirichlet L-function, Don Zagier, Donald Knuth, Ernst Kummer, Euler number, Euler summation, Euler–Maclaurin formula, Eulerian number, Even and odd functions, Exotic sphere, Falling and rising factorials, Faulhaber's formula, Fermat's Last Theorem, Fibonacci Quarterly, ..., Fundamental theorem of calculus, Generating function, Genocchi number, Gottfried Wilhelm Leibniz, Harmonic number, Harmonic progression (mathematics), Herbrand–Ribet theorem, Hurwitz zeta function, Hyperbolic function, Ibn al-Haytham, Ideal class group, Imaginary unit, Implementation, Inclusion–exclusion principle, Integral, Iverson bracket, Jacob Bernoulli, Johann Faulhaber, Karl Georg Christian von Staudt, Kronecker delta, Kummer's congruence, Kummer–Vandiver conjecture, Laurent series, Leonhard Euler, Leopold Kronecker, Logical equivalence, Marcel Riesz, Mathematics, Mersenne prime, National Institute of Standards and Technology, Noam Elkies, Number theory, Orientability, P-adic L-function, P-adic number, Parallelizable manifold, Pascal's triangle, Philipp Ludwig von Seidel, Pierre de Fermat, Poly-Bernoulli number, Polynomial, Prime number, Probability distribution, Project Gutenberg, Pythagoras, Q-analog, Rahul Pandharipande, Rational number, Regular prime, Riemann hypothesis, Riemann zeta function, Riesz function, Ronald Graham, SageMath, Scientific notation, Seki Takakazu, Sequence, Simon Plouffe, Special values of L-functions, Square pyramidal number, Square-free element, Srinivasa Ramanujan, Stirling numbers of the first kind, Stirling numbers of the second kind, Stirling polynomials, Stirling's approximation, Summation, Sums of powers, Taylor series, Thomas Clausen (mathematician), Thomas Harriot, Triangular number, Trigamma function, Trigonometric functions, Umbral calculus, Uniform distribution (continuous), Von Staudt–Clausen theorem, Wolfram Mathematica, Yuri Matiyasevich. Expand index (79 more) »

Abraham de Moivre

Abraham de Moivre (26 May 166727 November 1754) was a French mathematician known for de Moivre's formula, a formula that links complex numbers and trigonometry, and for his work on the normal distribution and probability theory.

New!!: Bernoulli number and Abraham de Moivre · See more »

Ada Lovelace

Augusta Ada King-Noel, Countess of Lovelace (née Byron; 10 December 1815 – 27 November 1852) was an English mathematician and writer, chiefly known for her work on Charles Babbage's proposed mechanical general-purpose computer, the Analytical Engine.

New!!: Bernoulli number and Ada Lovelace · See more »

Agoh–Giuga conjecture

In number theory the Agoh–Giuga conjecture on the Bernoulli numbers Bk postulates that p is a prime number if and only if It is named after Takashi Agoh and Giuseppe Giuga.

New!!: Bernoulli number and Agoh–Giuga conjecture · See more »

Al-Karaji

(c. 953 – c. 1029) was a 10th-century Persian mathematician and engineer who flourished at Baghdad.

New!!: Bernoulli number and Al-Karaji · See more »

Algebraic number

An algebraic number is any complex number (including real numbers) that is a root of a non-zero polynomial (that is, a value which causes the polynomial to equal 0) in one variable with rational coefficients (or equivalently – by clearing denominators – with integer coefficients).

New!!: Bernoulli number and Algebraic number · See more »

Algorithm

In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.

New!!: Bernoulli number and Algorithm · See more »

Alternating permutation

In combinatorial mathematics, an alternating permutation (or zigzag permutation) of the set is an arrangement of those numbers so that each entry is alternately greater or less than the preceding entry.

New!!: Bernoulli number and Alternating permutation · See more »

Analytical Engine

The Analytical Engine was a proposed mechanical general-purpose computer designed by English mathematician and computer pioneer Charles Babbage.

New!!: Bernoulli number and Analytical Engine · See more »

Ankeny–Artin–Chowla congruence

In number theory, the Ankeny–Artin–Chowla congruence is a result published in 1953 by N. C. Ankeny, Emil Artin and S. Chowla.

New!!: Bernoulli number and Ankeny–Artin–Chowla congruence · See more »

Antiderivative

In calculus, an antiderivative, primitive function, primitive integral or indefinite integral of a function is a differentiable function whose derivative is equal to the original function.

New!!: Bernoulli number and Antiderivative · See more »

Archimedes

Archimedes of Syracuse (Ἀρχιμήδης) was a Greek mathematician, physicist, engineer, inventor, and astronomer.

New!!: Bernoulli number and Archimedes · See more »

Ars Conjectandi

Ars Conjectandi (Latin for "The Art of Conjecturing") is a book on combinatorics and mathematical probability written by Jacob Bernoulli and published in 1713, eight years after his death, by his nephew, Niklaus Bernoulli.

New!!: Bernoulli number and Ars Conjectandi · See more »

Aryabhata

Aryabhata (IAST) or Aryabhata I (476–550 CE) was the first of the major mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy.

New!!: Bernoulli number and Aryabhata · See more »

Asymptotic analysis

In mathematical analysis, asymptotic analysis, also known as asymptotics, is a method of describing limiting behavior.

New!!: Bernoulli number and Asymptotic analysis · See more »

Asymptotic expansion

In mathematics, an asymptotic expansion, asymptotic series or Poincaré expansion (after Henri Poincaré) is a formal series of functions which has the property that truncating the series after a finite number of terms provides an approximation to a given function as the argument of the function tends towards a particular, often infinite, point.

New!!: Bernoulli number and Asymptotic expansion · See more »

Bernoulli polynomials

In mathematics, the Bernoulli polynomials, named after Jacob Bernoulli, occur in the study of many special functions and, in particular the Riemann zeta function and the Hurwitz zeta function.

New!!: Bernoulli number and Bernoulli polynomials · See more »

Big O notation

Big O notation is a mathematical notation that describes the limiting behaviour of a function when the argument tends towards a particular value or infinity.

New!!: Bernoulli number and Big O notation · See more »

Binomial coefficient

In mathematics, any of the positive integers that occurs as a coefficient in the binomial theorem is a binomial coefficient.

New!!: Bernoulli number and Binomial coefficient · See more »

Blaise Pascal

Blaise Pascal (19 June 1623 – 19 August 1662) was a French mathematician, physicist, inventor, writer and Catholic theologian.

New!!: Bernoulli number and Blaise Pascal · See more »

Boustrophedon transform

In mathematics, the boustrophedon transform is a procedure which maps one sequence to another.

New!!: Bernoulli number and Boustrophedon transform · See more »

Carl Gustav Jacob Jacobi

Carl Gustav Jacob Jacobi (10 December 1804 – 18 February 1851) was a German mathematician, who made fundamental contributions to elliptic functions, dynamics, differential equations, and number theory.

New!!: Bernoulli number and Carl Gustav Jacob Jacobi · See more »

Charles Babbage

Charles Babbage (26 December 1791 – 18 October 1871) was an English polymath.

New!!: Bernoulli number and Charles Babbage · See more »

Chinese remainder theorem

The Chinese remainder theorem is a theorem of number theory, which states that if one knows the remainders of the Euclidean division of an integer by several integers, then one can determine uniquely the remainder of the division of by the product of these integers, under the condition that the divisors are pairwise coprime.

New!!: Bernoulli number and Chinese remainder theorem · See more »

Closed manifold

In mathematics, a closed manifold is a type of topological space, namely a compact manifold without boundary.

New!!: Bernoulli number and Closed manifold · See more »

Closed-form expression

In mathematics, a closed-form expression is a mathematical expression that can be evaluated in a finite number of operations.

New!!: Bernoulli number and Closed-form expression · See more »

Coefficient

In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series or any expression; it is usually a number, but may be any expression.

New!!: Bernoulli number and Coefficient · See more »

Computational complexity theory

Computational complexity theory is a branch of the theory of computation in theoretical computer science that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other.

New!!: Bernoulli number and Computational complexity theory · See more »

Computer program

A computer program is a collection of instructions for performing a specific task that is designed to solve a specific class of problems.

New!!: Bernoulli number and Computer program · See more »

Converse relation

In mathematics, the converse relation, or transpose, of a binary relation is the relation that occurs when the order of the elements is switched in the relation.

New!!: Bernoulli number and Converse relation · See more »

Cumulant

In probability theory and statistics, the cumulants of a probability distribution are a set of quantities that provide an alternative to the moments of the distribution.

New!!: Bernoulli number and Cumulant · See more »

Cyclotomic field

In number theory, a cyclotomic field is a number field obtained by adjoining a complex primitive root of unity to, the field of rational numbers.

New!!: Bernoulli number and Cyclotomic field · See more »

Désiré André

Désiré André (André Antoine Désiré) (March 29, 1840, Lyon – September 12, 1917, Paris) was a French mathematician, best known for his work on Catalan numbers and alternating permutations.

New!!: Bernoulli number and Désiré André · See more »

Differentiable manifold

In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a linear space to allow one to do calculus.

New!!: Bernoulli number and Differentiable manifold · See more »

Digamma function

In mathematics, the digamma function is defined as the logarithmic derivative of the gamma function: It is the first of the polygamma functions.

New!!: Bernoulli number and Digamma function · See more »

Dimension

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.

New!!: Bernoulli number and Dimension · See more »

Dirichlet character

In number theory, Dirichlet characters are certain arithmetic functions which arise from completely multiplicative characters on the units of \mathbb Z / k \mathbb Z. Dirichlet characters are used to define Dirichlet ''L''-functions, which are meromorphic functions with a variety of interesting analytic properties.

New!!: Bernoulli number and Dirichlet character · See more »

Dirichlet L-function

In mathematics, a Dirichlet L-series is a function of the form Here χ is a Dirichlet character and s a complex variable with real part greater than 1.

New!!: Bernoulli number and Dirichlet L-function · See more »

Don Zagier

Don Bernard Zagier (born 29 June 1951) is an American mathematician whose main area of work is number theory.

New!!: Bernoulli number and Don Zagier · See more »

Donald Knuth

Donald Ervin Knuth (born January 10, 1938) is an American computer scientist, mathematician, and professor emeritus at Stanford University.

New!!: Bernoulli number and Donald Knuth · See more »

Ernst Kummer

Ernst Eduard Kummer (29 January 1810 – 14 May 1893) was a German mathematician.

New!!: Bernoulli number and Ernst Kummer · See more »

Euler number

In mathematics, the Euler numbers are a sequence En of integers defined by the Taylor series expansion where is the hyperbolic cosine.

New!!: Bernoulli number and Euler number · See more »

Euler summation

In the mathematics of convergent and divergent series, Euler summation is a summability method.

New!!: Bernoulli number and Euler summation · See more »

Euler–Maclaurin formula

In mathematics, the Euler–Maclaurin formula provides a powerful connection between integrals (see calculus) and sums.

New!!: Bernoulli number and Euler–Maclaurin formula · See more »

Eulerian number

In combinatorics, the Eulerian number A(n, m), is the number of permutations of the numbers 1 to n in which exactly m elements are greater than the previous element (permutations with m "ascents").

New!!: Bernoulli number and Eulerian number · See more »

Even and odd functions

In mathematics, even functions and odd functions are functions which satisfy particular symmetry relations, with respect to taking additive inverses.

New!!: Bernoulli number and Even and odd functions · See more »

Exotic sphere

In differential topology, an exotic sphere is a differentiable manifold M that is homeomorphic but not diffeomorphic to the standard Euclidean n-sphere.

New!!: Bernoulli number and Exotic sphere · See more »

Falling and rising factorials

In mathematics, the falling factorial (sometimes called the descending factorial, falling sequential product, or lower factorial) is defined as The rising factorial (sometimes called the Pochhammer function, Pochhammer polynomial, ascending factorial, (A reprint of the 1950 edition by Chelsea Publishing Co.) rising sequential product, or upper factorial) is defined as The value of each is taken to be 1 (an empty product) when n.

New!!: Bernoulli number and Falling and rising factorials · See more »

Faulhaber's formula

In mathematics, Faulhaber's formula, named after Johann Faulhaber, expresses the sum of the p-th powers of the first n positive integers as a (p + 1)th-degree polynomial function of n, the coefficients involving Bernoulli numbers Bj, in the form submitted by Jacob Bernoulli and published in 1713: where p^\underline.

New!!: Bernoulli number and Faulhaber's formula · See more »

Fermat's Last Theorem

In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers,, and satisfy the equation for any integer value of greater than 2.

New!!: Bernoulli number and Fermat's Last Theorem · See more »

Fibonacci Quarterly

The Fibonacci Quarterly is a scientific journal on mathematical topics related to the Fibonacci numbers, published four times per year.

New!!: Bernoulli number and Fibonacci Quarterly · See more »

Fundamental theorem of calculus

The fundamental theorem of calculus is a theorem that links the concept of differentiating a function with the concept of integrating a function.

New!!: Bernoulli number and Fundamental theorem of calculus · See more »

Generating function

In mathematics, a generating function is a way of encoding an infinite sequence of numbers (an) by treating them as the coefficients of a power series.

New!!: Bernoulli number and Generating function · See more »

Genocchi number

In mathematics, the Genocchi numbers Gn, named after Angelo Genocchi, are a sequence of integers that satisfy the relation \frac.

New!!: Bernoulli number and Genocchi number · See more »

Gottfried Wilhelm Leibniz

Gottfried Wilhelm (von) Leibniz (or; Leibnitz; – 14 November 1716) was a German polymath and philosopher who occupies a prominent place in the history of mathematics and the history of philosophy.

New!!: Bernoulli number and Gottfried Wilhelm Leibniz · See more »

Harmonic number

In mathematics, the -th harmonic number is the sum of the reciprocals of the first natural numbers: Harmonic numbers are related to the harmonic mean in that the -th harmonic number is also times the reciprocal of the harmonic mean of the first positive integers.

New!!: Bernoulli number and Harmonic number · See more »

Harmonic progression (mathematics)

In mathematics, a harmonic progression (or harmonic sequence) is a progression formed by taking the reciprocals of an arithmetic progression.

New!!: Bernoulli number and Harmonic progression (mathematics) · See more »

Herbrand–Ribet theorem

In mathematics, the Herbrand–Ribet theorem is a result on the class group of certain number fields.

New!!: Bernoulli number and Herbrand–Ribet theorem · See more »

Hurwitz zeta function

In mathematics, the Hurwitz zeta function, named after Adolf Hurwitz, is one of the many zeta functions.

New!!: Bernoulli number and Hurwitz zeta function · See more »

Hyperbolic function

In mathematics, hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions.

New!!: Bernoulli number and Hyperbolic function · See more »

Ibn al-Haytham

Hasan Ibn al-Haytham (Latinized Alhazen; full name أبو علي، الحسن بن الحسن بن الهيثم) was an Arab mathematician, astronomer, and physicist of the Islamic Golden Age.

New!!: Bernoulli number and Ibn al-Haytham · See more »

Ideal class group

In number theory, the ideal class group (or class group) of an algebraic number field is the quotient group where is the group of fractional ideals of the ring of integers of, and is its subgroup of principal ideals.

New!!: Bernoulli number and Ideal class group · See more »

Imaginary unit

The imaginary unit or unit imaginary number is a solution to the quadratic equation.

New!!: Bernoulli number and Imaginary unit · See more »

Implementation

Implementation is the realization of an application, or execution of a plan, idea, model, design, specification, standard, algorithm, or policy.

New!!: Bernoulli number and Implementation · See more »

Inclusion–exclusion principle

In combinatorics (combinatorial mathematics), the inclusion–exclusion principle is a counting technique which generalizes the familiar method of obtaining the number of elements in the union of two finite sets; symbolically expressed as where A and B are two finite sets and |S| indicates the cardinality of a set S (which may be considered as the number of elements of the set, if the set is finite).

New!!: Bernoulli number and Inclusion–exclusion principle · See more »

Integral

In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

New!!: Bernoulli number and Integral · See more »

Iverson bracket

In mathematics, the Iverson bracket, named after Kenneth E. Iverson, is a notation that generalises the Kronecker delta.

New!!: Bernoulli number and Iverson bracket · See more »

Jacob Bernoulli

Jacob Bernoulli (also known as James or Jacques; – 16 August 1705) was one of the many prominent mathematicians in the Bernoulli family.

New!!: Bernoulli number and Jacob Bernoulli · See more »

Johann Faulhaber

Johann Faulhaber (5 May 1580 – 10 September 1635) was a German mathematician.

New!!: Bernoulli number and Johann Faulhaber · See more »

Karl Georg Christian von Staudt

Karl Georg Christian von Staudt (24 January 1798 – 1 June 1867) was a German mathematician who used synthetic geometry to provide a foundation for arithmetic.

New!!: Bernoulli number and Karl Georg Christian von Staudt · See more »

Kronecker delta

In mathematics, the Kronecker delta (named after Leopold Kronecker) is a function of two variables, usually just non-negative integers.

New!!: Bernoulli number and Kronecker delta · See more »

Kummer's congruence

In mathematics, Kummer's congruences are some congruences involving Bernoulli numbers, found by.

New!!: Bernoulli number and Kummer's congruence · See more »

Kummer–Vandiver conjecture

In mathematics, the Kummer–Vandiver conjecture, or Vandiver conjecture, states that a prime p does not divide the class number hK of the maximal real subfield K.

New!!: Bernoulli number and Kummer–Vandiver conjecture · See more »

Laurent series

In mathematics, the Laurent series of a complex function f(z) is a representation of that function as a power series which includes terms of negative degree.

New!!: Bernoulli number and Laurent series · See more »

Leonhard Euler

Leonhard Euler (Swiss Standard German:; German Standard German:; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer, who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory.

New!!: Bernoulli number and Leonhard Euler · See more »

Leopold Kronecker

Leopold Kronecker (7 December 1823 – 29 December 1891) was a German mathematician who worked on number theory, algebra and logic.

New!!: Bernoulli number and Leopold Kronecker · See more »

Logical equivalence

In logic, statements p and q are logically equivalent if they have the same logical content.

New!!: Bernoulli number and Logical equivalence · See more »

Marcel Riesz

Marcel Riesz (Riesz Marcell; 16 November 1886 – 4 September 1969) was a Hungarian-born mathematician, known for work on summation methods, potential theory, and other parts of analysis, as well as number theory, partial differential equations, and Clifford algebras.

New!!: Bernoulli number and Marcel Riesz · See more »

Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

New!!: Bernoulli number and Mathematics · See more »

Mersenne prime

In mathematics, a Mersenne prime is a prime number that is one less than a power of two.

New!!: Bernoulli number and Mersenne prime · See more »

National Institute of Standards and Technology

The National Institute of Standards and Technology (NIST) is one of the oldest physical science laboratories in the United States.

New!!: Bernoulli number and National Institute of Standards and Technology · See more »

Noam Elkies

Noam David Elkies (born August 25, 1966) is an American mathematician and professor of mathematics at Harvard University.

New!!: Bernoulli number and Noam Elkies · See more »

Number theory

Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers.

New!!: Bernoulli number and Number theory · See more »

Orientability

In mathematics, orientability is a property of surfaces in Euclidean space that measures whether it is possible to make a consistent choice of surface normal vector at every point.

New!!: Bernoulli number and Orientability · See more »

P-adic L-function

In mathematics, a p-adic zeta function, or more generally a p-adic L-function, is a function analogous to the Riemann zeta function, or more general ''L''-functions, but whose domain and target are p-adic (where p is a prime number).

New!!: Bernoulli number and P-adic L-function · See more »

P-adic number

In mathematics, the -adic number system for any prime number extends the ordinary arithmetic of the rational numbers in a different way from the extension of the rational number system to the real and complex number systems.

New!!: Bernoulli number and P-adic number · See more »

Parallelizable manifold

In mathematics, a differentiable manifold M of dimension n is called parallelizable if there exist smooth vector fields on the manifold, such that at any point p of M the tangent vectors provide a basis of the tangent space at p. Equivalently, the tangent bundle is a trivial bundle, so that the associated principal bundle of linear frames has a section on M. A particular choice of such a basis of vector fields on M is called a parallelization (or an absolute parallelism) of M.

New!!: Bernoulli number and Parallelizable manifold · See more »

Pascal's triangle

In mathematics, Pascal's triangle is a triangular array of the binomial coefficients.

New!!: Bernoulli number and Pascal's triangle · See more »

Philipp Ludwig von Seidel

Philipp Ludwig von Seidel (23 October 1821 in Zweibrücken, Germany – 13 August 1896 in Munich, German Empire) was a German mathematician.

New!!: Bernoulli number and Philipp Ludwig von Seidel · See more »

Pierre de Fermat

Pierre de Fermat (Between 31 October and 6 December 1607 – 12 January 1665) was a French lawyer at the Parlement of Toulouse, France, and a mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality.

New!!: Bernoulli number and Pierre de Fermat · See more »

Poly-Bernoulli number

In mathematics, poly-Bernoulli numbers, denoted as B_^, were defined by M. Kaneko as where Li is the polylogarithm.

New!!: Bernoulli number and Poly-Bernoulli number · See more »

Polynomial

In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

New!!: Bernoulli number and Polynomial · See more »

Prime number

A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.

New!!: Bernoulli number and Prime number · See more »

Probability distribution

In probability theory and statistics, a probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.

New!!: Bernoulli number and Probability distribution · See more »

Project Gutenberg

Project Gutenberg (PG) is a volunteer effort to digitize and archive cultural works, to "encourage the creation and distribution of eBooks".

New!!: Bernoulli number and Project Gutenberg · See more »

Pythagoras

Pythagoras of Samos was an Ionian Greek philosopher and the eponymous founder of the Pythagoreanism movement.

New!!: Bernoulli number and Pythagoras · See more »

Q-analog

In mathematics, a q-analog of a theorem, identity or expression is a generalization involving a new parameter q that returns the original theorem, identity or expression in the limit as.

New!!: Bernoulli number and Q-analog · See more »

Rahul Pandharipande

Rahul Pandharipande (born 1969) is a mathematician who is currently a professor of mathematics at the Swiss Federal Institute of Technology Zürich (ETH) working in algebraic geometry.

New!!: Bernoulli number and Rahul Pandharipande · See more »

Rational number

In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.

New!!: Bernoulli number and Rational number · See more »

Regular prime

In number theory, a regular prime is a special kind of prime number, defined by Ernst Kummer in 1850 to prove certain cases of Fermat's Last Theorem.

New!!: Bernoulli number and Regular prime · See more »

Riemann hypothesis

In mathematics, the Riemann hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part.

New!!: Bernoulli number and Riemann hypothesis · See more »

Riemann zeta function

The Riemann zeta function or Euler–Riemann zeta function,, is a function of a complex variable s that analytically continues the sum of the Dirichlet series which converges when the real part of is greater than 1.

New!!: Bernoulli number and Riemann zeta function · See more »

Riesz function

In mathematics, the Riesz function is an entire function defined by Marcel Riesz in connection with the Riemann hypothesis, by means of the power series If we set F(x).

New!!: Bernoulli number and Riesz function · See more »

Ronald Graham

Ronald Lewis "Ron" Graham (born October 31, 1935) is an American mathematician credited by the American Mathematical Society as being "one of the principal architects of the rapid development worldwide of discrete mathematics in recent years".

New!!: Bernoulli number and Ronald Graham · See more »

SageMath

SageMath (previously Sage or SAGE, "System for Algebra and Geometry Experimentation") is a computer algebra system with features covering many aspects of mathematics, including algebra, combinatorics, graph theory, numerical analysis, number theory, calculus and statistics.

New!!: Bernoulli number and SageMath · See more »

Scientific notation

Scientific notation (also referred to as scientific form or standard index form, or standard form in the UK) is a way of expressing numbers that are too big or too small to be conveniently written in decimal form.

New!!: Bernoulli number and Scientific notation · See more »

Seki Takakazu

, also known as,Selin, was a Japanese mathematician and author of the Edo period.

New!!: Bernoulli number and Seki Takakazu · See more »

Sequence

In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed.

New!!: Bernoulli number and Sequence · See more »

Simon Plouffe

Simon Plouffe (born June 11, 1956, Saint-Jovite, Quebec) is a mathematician who discovered the Bailey–Borwein–Plouffe formula (BBP algorithm) which permits the computation of the nth binary digit of π, in 1995.

New!!: Bernoulli number and Simon Plouffe · See more »

Special values of L-functions

In mathematics, the study of special values of L-functions is a subfield of number theory devoted to generalising formulae such as the Leibniz formula for pi, namely by the recognition that expression on the left-hand side is also L(1) where L(s) is the Dirichlet L-function for the Gaussian field.

New!!: Bernoulli number and Special values of L-functions · See more »

Square pyramidal number

In mathematics, a pyramid number, or square pyramidal number, is a figurate number that represents the number of stacked spheres in a pyramid with a square base.

New!!: Bernoulli number and Square pyramidal number · See more »

Square-free element

In mathematics, a square-free element is an element r of a unique factorization domain R that is not divisible by a non-trivial square.

New!!: Bernoulli number and Square-free element · See more »

Srinivasa Ramanujan

Srinivasa Ramanujan (22 December 188726 April 1920) was an Indian mathematician who lived during the British Rule in India. Though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to mathematical problems considered to be unsolvable.

New!!: Bernoulli number and Srinivasa Ramanujan · See more »

Stirling numbers of the first kind

In mathematics, especially in combinatorics, Stirling numbers of the first kind arise in the study of permutations.

New!!: Bernoulli number and Stirling numbers of the first kind · See more »

Stirling numbers of the second kind

In mathematics, particularly in combinatorics, a Stirling number of the second kind (or Stirling partition number) is the number of ways to partition a set of n objects into k non-empty subsets and is denoted by S(n,k) or \textstyle \lbrace\rbrace.

New!!: Bernoulli number and Stirling numbers of the second kind · See more »

Stirling polynomials

In mathematics, the Stirling polynomials are a family of polynomials that generalize important sequences of numbers appearing in combinatorics and analysis, which are closely related to the Stirling numbers, the Bernoulli numbers, and the generalized Bernoulli polynomials.

New!!: Bernoulli number and Stirling polynomials · See more »

Stirling's approximation

In mathematics, Stirling's approximation (or Stirling's formula) is an approximation for factorials.

New!!: Bernoulli number and Stirling's approximation · See more »

Summation

In mathematics, summation (capital Greek sigma symbol: ∑) is the addition of a sequence of numbers; the result is their sum or total.

New!!: Bernoulli number and Summation · See more »

Sums of powers

In mathematics and statistics, sums of powers occur in a number of contexts.

New!!: Bernoulli number and Sums of powers · See more »

Taylor series

In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point.

New!!: Bernoulli number and Taylor series · See more »

Thomas Clausen (mathematician)

Thomas Clausen (January 16, 1801, Snogbæk, Sottrup Municipality, Duchy of Schleswig (now Denmark) – May 23, 1885, Derpt, Imperial Russia (now Estonia)) was a Danish mathematician and astronomer.

New!!: Bernoulli number and Thomas Clausen (mathematician) · See more »

Thomas Harriot

Thomas Harriot (Oxford, c. 1560 – London, 2 July 1621), also spelled Harriott, Hariot or Heriot, was an English astronomer, mathematician, ethnographer and translator who made advances within the scientific field.

New!!: Bernoulli number and Thomas Harriot · See more »

Triangular number

A triangular number or triangle number counts objects arranged in an equilateral triangle, as in the diagram on the right.

New!!: Bernoulli number and Triangular number · See more »

Trigamma function

In mathematics, the trigamma function, denoted, is the second of the polygamma functions, and is defined by It follows from this definition that where is the digamma function.

New!!: Bernoulli number and Trigamma function · See more »

Trigonometric functions

In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are functions of an angle.

New!!: Bernoulli number and Trigonometric functions · See more »

Umbral calculus

In mathematics before the 1970s, the term umbral calculus referred to the surprising similarity between seemingly unrelated polynomial equations and certain shadowy techniques used to 'prove' them.

New!!: Bernoulli number and Umbral calculus · See more »

Uniform distribution (continuous)

In probability theory and statistics, the continuous uniform distribution or rectangular distribution is a family of symmetric probability distributions such that for each member of the family, all intervals of the same length on the distribution's support are equally probable.

New!!: Bernoulli number and Uniform distribution (continuous) · See more »

Von Staudt–Clausen theorem

In number theory, the von Staudt–Clausen theorem is a result determining the fractional part of Bernoulli numbers, found independently by and.

New!!: Bernoulli number and Von Staudt–Clausen theorem · See more »

Wolfram Mathematica

Wolfram Mathematica (usually termed Mathematica) is a modern technical computing system spanning most areas of technical computing — including neural networks, machine learning, image processing, geometry, data science, visualizations, and others.

New!!: Bernoulli number and Wolfram Mathematica · See more »

Yuri Matiyasevich

Yuri Vladimirovich Matiyasevich, (Ю́рий Влади́мирович Матиясе́вич; born March 2, 1947, in Leningrad) is a Russian mathematician and computer scientist.

New!!: Bernoulli number and Yuri Matiyasevich · See more »

Redirects here:

Akiyama-Tanigawa algorithm, Akiyama–Tanigawa algorithm, Bernouilli number, Bernouilli numbers, Bernoulli Numbers, Bernoulli numbers, First Bernoulli numbers, Generalised Bernoulli number, Generalized Bernoulli number, Generalized Bernoulli numbers, Generalized bernoulli number, Mohammed Altoumaimi, Second Bernoulli numbers, Seidel triangle.

References

[1] https://en.wikipedia.org/wiki/Bernoulli_number

OutgoingIncoming
Hey! We are on Facebook now! »