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Apéry's constant

Index Apéry's constant

In mathematics, at the intersection of number theory and special functions, Apéry's constant is defined as the number where is the Riemann zeta function. [1]

46 relations: Adrien-Marie Legendre, Almost integer, Apéry's theorem, Basel problem, Binary number, Bit, Catalan's constant, Constant (mathematics), Continued fraction, Coprime integers, Debye model, Decimal, Discrete Applied Mathematics, France, Gamma function, Gyromagnetic ratio, Hexadecimal, Irrational number, Johan Jensen (mathematician), L (complexity), Legendre chi function, Legendre polynomials, Leonhard Euler, List of sums of reciprocals, Mathematician, Mathematics, Multiplicative inverse, Natural number, Number theory, Periodic continued fraction, Polygamma function, Probability, Quantum electrodynamics, Random minimum spanning tree, Riemann zeta function, Roger Apéry, Simon Plouffe, Special functions, Springer Science+Business Media, Srinivasa Ramanujan, Stefan–Boltzmann law, The Mathematical Intelligencer, Thomas Joannes Stieltjes, Time complexity, Transcendental number, Wadim Zudilin.

Adrien-Marie Legendre

Adrien-Marie Legendre (18 September 1752 – 10 January 1833) was a French mathematician.

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Almost integer

In recreational mathematics, an almost integer (or near-integer) is any number that is not an integer but is very close to one.

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Apéry's theorem

In mathematics, Apéry's theorem is a result in number theory that states the Apéry's constant ζ(3) is irrational.

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Basel problem

The Basel problem is a problem in mathematical analysis with relevance to number theory, first posed by Pietro Mengoli in 1644 and solved by Leonhard Euler in 1734 and read on 5 December 1735 in ''The Saint Petersburg Academy of Sciences''.

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Binary number

In mathematics and digital electronics, a binary number is a number expressed in the base-2 numeral system or binary numeral system, which uses only two symbols: typically 0 (zero) and 1 (one).

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Bit

The bit (a portmanteau of binary digit) is a basic unit of information used in computing and digital communications.

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Catalan's constant

In mathematics, Catalan's constant, which appears in combinatorics, is defined by where is the Dirichlet beta function.

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Constant (mathematics)

In mathematics, the adjective constant means non-varying.

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Continued fraction

In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on.

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Coprime integers

In number theory, two integers and are said to be relatively prime, mutually prime, or coprime (also written co-prime) if the only positive integer (factor) that divides both of them is 1.

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Debye model

In thermodynamics and solid state physics, the Debye model is a method developed by Peter Debye in 1912 for estimating the phonon contribution to the specific heat (heat capacity) in a solid.

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Decimal

The decimal numeral system (also called base-ten positional numeral system, and occasionally called denary) is the standard system for denoting integer and non-integer numbers.

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Discrete Applied Mathematics

Discrete Applied Mathematics is a peer-reviewed academic journal in mathematics, published by Elsevier.

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France

France, officially the French Republic (République française), is a sovereign state whose territory consists of metropolitan France in Western Europe, as well as several overseas regions and territories.

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Gamma function

In mathematics, the gamma function (represented by, the capital Greek alphabet letter gamma) is an extension of the factorial function, with its argument shifted down by 1, to real and complex numbers.

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Gyromagnetic ratio

In physics, the gyromagnetic ratio (also sometimes known as the magnetogyric ratio in other disciplines) of a particle or system is the ratio of its magnetic moment to its angular momentum, and it is often denoted by the symbol γ, gamma.

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Hexadecimal

In mathematics and computing, hexadecimal (also base, or hex) is a positional numeral system with a radix, or base, of 16.

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Irrational number

In mathematics, the irrational numbers are all the real numbers which are not rational numbers, the latter being the numbers constructed from ratios (or fractions) of integers.

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Johan Jensen (mathematician)

Johan Ludwig William Valdemar Jensen, mostly known as Johan Jensen (8 May 1859 – 5 March 1925), was a Danish mathematician and engineer.

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L (complexity)

In computational complexity theory, L (also known as LSPACE or DLOGSPACE) is the complexity class containing decision problems that can be solved by a deterministic Turing machine using a logarithmic amount of writable memory space.

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Legendre chi function

In mathematics, the Legendre chi function is a special function whose Taylor series is also a Dirichlet series, given by \chi_\nu(z).

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Legendre polynomials

In mathematics, Legendre functions are solutions to Legendre's differential equation: They are named after Adrien-Marie Legendre.

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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.

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List of sums of reciprocals

In mathematics and especially number theory, the sum of reciprocals generally is computed for the reciprocals of some or all of the positive integers (counting numbers)—that is, it is generally the sum of unit fractions.

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Mathematician

A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.

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Mathematics

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

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Multiplicative inverse

In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1.

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Natural number

In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").

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Number theory

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

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Periodic continued fraction

In mathematics, an infinite periodic continued fraction is a continued fraction that can be placed in the form x.

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Polygamma function

In mathematics, the polygamma function of order is a meromorphic function on '''ℂ''' and defined as the th derivative of the logarithm of the gamma function: Thus holds where is the digamma function and is the gamma function.

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Probability

Probability is the measure of the likelihood that an event will occur.

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Quantum electrodynamics

In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics.

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Random minimum spanning tree

In mathematics, a random minimum spanning tree may be formed by assigning random weights from some distribution to the edges of an undirected graph, and then constructing the minimum spanning tree of the graph.

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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.

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Roger Apéry

Roger Apéry (14 November 1916, Rouen – 18 December 1994, Caen) was a Greek-French mathematician most remembered for Apéry's theorem, which states that ζ(3) is an irrational number.

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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.

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Special functions

Special functions are particular mathematical functions which have more or less established names and notations due to their importance in mathematical analysis, functional analysis, physics, or other applications.

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Springer Science+Business Media

Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.

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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.

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Stefan–Boltzmann law

The Stefan–Boltzmann law describes the power radiated from a black body in terms of its temperature.

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The Mathematical Intelligencer

The Mathematical Intelligencer is a mathematical journal published by Springer Verlag that aims at a conversational and scholarly tone, rather than the technical and specialist tone more common among academic journals.

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Thomas Joannes Stieltjes

Thomas Joannes Stieltjes (29 December 1856 – 31 December 1894) was a Dutch mathematician.

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Time complexity

In computer science, the time complexity is the computational complexity that describes the amount of time it takes to run an algorithm.

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Transcendental number

In mathematics, a transcendental number is a real or complex number that is not algebraic—that is, it is not a root of a nonzero polynomial equation with integer (or, equivalently, rational) coefficients.

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Wadim Zudilin

Wadim Zudilin (Вадим Валентинович Зудилин) is a Russian number theorist who is active in studying hypergeometric functions and zeta constants.

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References

[1] https://en.wikipedia.org/wiki/Apéry's_constant

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