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# Euler–Mascheroni constant

The Euler–Mascheroni constant (also called Euler's constant) is a mathematical constant recurring in analysis and number theory, usually denoted by the lowercase Greek letter gamma. [1]

92 relations: Algebraic number, American Mathematical Monthly, Augustus De Morgan, Barnes G-function, Bessel function, Beta function, Binary logarithm, Binary number, Bulletin of the American Mathematical Society, Carl Anton Bretschneider, Carl Friedrich Gauss, Carl Johan Malmsten, Charles Jean de la Vallée Poussin, Chi-squared distribution, Continued fraction, Coupon collector's problem, Decimal, Derivative, Digamma function, Dimensional regularization, Divisor function, Donald Knuth, Early Modern Switzerland, Edwin McMillan, Entropy (information theory), Ernesto Cesàro, Ernst Kummer, Eugène Charles Catalan, Euler's totient function, Exponential integral, Feynman diagram, Floor and ceiling functions, Friedrich Bernhard Gottfried Nicolai, Gamma, Gamma function, Germany, Giovanni Vacca (mathematician), Greatest common divisor, Gregorio Fontana, Gregory coefficients, Gumbel distribution, Hadjicostas's formula, Harmonic number, Harmonic series (mathematics), Hexadecimal, Hurwitz zeta function, Hypergeometric function, If and only if, Infinite product, Integral, ... Expand index (42 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).

## American Mathematical Monthly

The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894.

## Augustus De Morgan

Augustus De Morgan (27 June 1806 – 18 March 1871) was a British mathematician and logician.

## Barnes G-function

In mathematics, the Barnes G-function G(z) is a function that is an extension of superfactorials to the complex numbers.

## Bessel function

Bessel functions, first defined by the mathematician Daniel Bernoulli and then generalized by Friedrich Bessel, are the canonical solutions of Bessel's differential equation for an arbitrary complex number, the order of the Bessel function.

## Beta function

In mathematics, the beta function, also called the Euler integral of the first kind, is a special function defined by for.

## Binary logarithm

In mathematics, the binary logarithm is the power to which the number must be raised to obtain the value.

## 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).

## Bulletin of the American Mathematical Society

The Bulletin of the American Mathematical Society is a quarterly mathematical journal published by the American Mathematical Society.

## Carl Anton Bretschneider

Carl Anton Bretschneider (27 May 1808 – 6 November 1878) was a mathematician from Gotha, Germany.

## Carl Friedrich Gauss

Johann Carl Friedrich Gauss (Gauß; Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields, including algebra, analysis, astronomy, differential geometry, electrostatics, geodesy, geophysics, magnetic fields, matrix theory, mechanics, number theory, optics and statistics.

## Carl Johan Malmsten

Carl Johan Malmsten (April 9, 1814 in Uddetorp, Skara County, Sweden – February 11, 1886 in Uppsala, Sweden) was a Swedish mathematician and politician.

## Charles Jean de la Vallée Poussin

Charles-Jean Étienne Gustave Nicolas Le Vieux, Baron de la Vallée Poussin (14 August 1866 – 2 March 1962) was a Belgian mathematician.

No description.

## 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.

## Coupon collector's problem

In probability theory, the coupon collector's problem describes the "collect all coupons and win" contests.

## 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.

## Derivative

The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).

## 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.

## Dimensional regularization

In theoretical physics, dimensional regularization is a method introduced by Giambiagi and Bollini as well as – independently and more comprehensively – by 't Hooft and Veltman for regularizing integrals in the evaluation of Feynman diagrams; in other words, assigning values to them that are meromorphic functions of a complex parameter d, the analytic continuation of the number of spacetime dimensions.

## Divisor function

In mathematics, and specifically in number theory, a divisor function is an arithmetic function related to the divisors of an integer.

## Donald Knuth

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

## Early Modern Switzerland

The early modern history of the Old Swiss Confederacy (Eidgenossenschaft, also known as the "Swiss Republic" or Republica Helvetiorum) and its constituent Thirteen Cantons encompasses the time of the Thirty Years' War (1618&ndash;1648) until the French invasion of 1798.

## Edwin McMillan

Edwin Mattison McMillan (September 18, 1907 – September 7, 1991) was an American physicist and Nobel laureate credited with being the first-ever to produce a transuranium element, neptunium.

## Entropy (information theory)

Information entropy is the average rate at which information is produced by a stochastic source of data.

## Ernesto Cesàro

Ernesto Cesàro (12 March 1859 &ndash; 12 September 1906) was an Italian mathematician who worked in the field of differential geometry.

## Ernst Kummer

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

## Eugène Charles Catalan

Eugène Charles Catalan (30 May 1814 – 14 February 1894) was a French and Belgian mathematician who worked on continued fractions, descriptive geometry, number theory and combinatorics.

## Euler's totient function

In number theory, Euler's totient function counts the positive integers up to a given integer that are relatively prime to.

## Exponential integral

In mathematics, the exponential integral Ei is a special function on the complex plane.

## Feynman diagram

In theoretical physics, Feynman diagrams are pictorial representations of the mathematical expressions describing the behavior of subatomic particles.

## Floor and ceiling functions

In mathematics and computer science, the floor function is the function that takes as input a real number x and gives as output the greatest integer less than or equal to x, denoted \operatorname(x).

## Friedrich Bernhard Gottfried Nicolai

Friedrich Bernhard Gottfried Nicolai (October 25, 1793 – June 4, 1846) was a German astronomer.

## Gamma

Gamma (uppercase, lowercase; gámma) is the third letter of the Greek alphabet.

## 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.

## Germany

Germany (Deutschland), officially the Federal Republic of Germany (Bundesrepublik Deutschland), is a sovereign state in central-western Europe.

## Giovanni Vacca (mathematician)

Giovanni Enrico Eugenio Vacca (18 November 1872 – 6 January 1953) was an Italian mathematician, Sinologist and historian of science.

## Greatest common divisor

In mathematics, the greatest common divisor (gcd) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers.

## Gregorio Fontana

Gregorio Fontana (7 December 1735 – 24 August 1803) was an Italian mathematician.

## Gregory coefficients

Gregory coefficients, also known as reciprocal logarithmic numbers, Bernoulli numbers of the second kind, or Cauchy numbers of the first kind,Ch.

## Gumbel distribution

In probability theory and statistics, the Gumbel distribution (Generalized Extreme Value distribution Type-I) is used to model the distribution of the maximum (or the minimum) of a number of samples of various distributions.

In mathematics, Hadjicostas's formula is a formula relating a certain double integral to values of the Gamma function and the Riemann zeta function.

## 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.

## Harmonic series (mathematics)

In mathematics, the harmonic series is the divergent infinite series: Its name derives from the concept of overtones, or harmonics in music: the wavelengths of the overtones of a vibrating string are,,, etc., of the string's fundamental wavelength.

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

## Hurwitz zeta function

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

## Hypergeometric function

In mathematics, the Gaussian or ordinary hypergeometric function 2F1(a,b;c;z) is a special function represented by the hypergeometric series, that includes many other special functions as specific or limiting cases.

## If and only if

In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements.

## Infinite product

In mathematics, for a sequence of complex numbers a1, a2, a3,...

## 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.

## 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.

## Italy

Italy (Italia), officially the Italian Republic (Repubblica Italiana), is a sovereign state in Europe.

James Whitbread Lee Glaisher FRS FRSE FRAS (5 November 1848, Lewisham – 7 December 1928, Cambridge), son of James Glaisher the meteorologist and Cecilia Glaisher the photographer, was a prolific English mathematician and astronomer.

## Johann Georg von Soldner

Johann Georg von Soldner (16 July 1776 in Feuchtwangen, Ansbach &ndash; 13 May 1833 in Bogenhausen, Munich) was a German physicist, mathematician and astronomer, first in Berlin and later in 1808 in Munich.

John Couch Adams (5 June 1819 – 21 January 1892) was a British mathematician and astronomer.

## John Wrench

John William Wrench, Jr. (October 13, 1911 – February 27, 2009) was an American mathematician who worked primarily in numerical analysis.

## Jonathan Borwein

Jonathan Michael Borwein (20 May 1951 &ndash; 2 August 2016) was a Scottish mathematician who held an appointment as Laureate Professor of mathematics at the University of Newcastle, Australia.

## Journal of Number Theory

The Journal of Number Theory is a mathematics journal that publishes a broad spectrum of original research in number theory.

## Karl Longin Zeller

Karl Longin Zeller (December 28, 1924, Šiauliai, Lithuania – July 20, 2006, Tübingen) was a German mathematician and computer scientist who worked in numerical analysis and approximation theory.

## Laplace transform

In mathematics, the Laplace transform is an integral transform named after its discoverer Pierre-Simon Laplace.

## 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.

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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.

## Limit of a sequence

As the positive integer n becomes larger and larger, the value n\cdot \sin\bigg(\frac1\bigg) becomes arbitrarily close to 1.

## Lorenzo Mascheroni

Lorenzo Mascheroni (May 13, 1750 – July 14, 1800) was an Italian mathematician.

## Mathematical analysis

Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.

## Mathematical constant

A mathematical constant is a special number that is "significantly interesting in some way".

## Mean

In mathematics, mean has several different definitions depending on the context.

## Meissel–Mertens constant

The Meissel–Mertens constant (named after Ernst Meissel and Franz Mertens), also referred to as Mertens constant, Kronecker's constant, Hadamard–de la Vallée-Poussin constant or the prime reciprocal constant, is a mathematical constant in number theory, defined as the limiting difference between the harmonic series summed only over the primes and the natural logarithm of the natural logarithm: \sum_ \frac - \ln(\ln n) \right).

## Mertens' theorems

In number theory, Mertens' theorems are three 1874 results related to the density of prime numbers proved by Franz Mertens.

## Michael Waterman

Michael Spencer Waterman (born June 28, 1942) is a Professor of Biology, Mathematics and Computer Science at the University of Southern California (USC), where he holds an Endowed Associates Chair in Biological Sciences, Mathematics and Computer Science.

## Natural logarithm

The natural logarithm of a number is its logarithm to the base of the mathematical constant ''e'', where e is an irrational and transcendental number approximately equal to.

## Niels Nielsen (mathematician)

Niels Nielsen (2 December 1865, in Ørslev – 16 September 1931, in Copenhagen) was a Danish mathematician who specialized in mathematical analysis.

## Number theory

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

## Periodic continued fraction

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

## 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.

## Quantum field theory

In theoretical physics, quantum field theory (QFT) is the theoretical framework for constructing quantum mechanical models of subatomic particles in particle physics and quasiparticles in condensed matter physics.

## 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.

## Rational zeta series

In mathematics, a rational zeta series is the representation of an arbitrary real number in terms of a series consisting of rational numbers and the Riemann zeta function or the Hurwitz zeta function.

## Renormalization

Renormalization is a collection of techniques in quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, that are used to treat infinities arising in calculated quantities by altering values of quantities to compensate for effects of their self-interactions.

## Richard P. Brent

Richard Peirce Brent (born 20 April 1946, Melbourne) is an Australian mathematician and computer scientist.

## 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.

## Series (mathematics)

In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity.

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.

## 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.

## Stieltjes constants

In mathematics, the Stieltjes constants are the numbers \gamma_k that occur in the Laurent series expansion of the Riemann zeta function: The constant \gamma_0.

## The Art of Computer Programming

The Art of Computer Programming (sometimes known by its initials TAOCP) is a comprehensive monograph written by Donald Knuth that covers many kinds of programming algorithms and their analysis.

## The Ramanujan Journal

The Ramanujan Journal is a peer-reviewed scientific journal covering all areas of mathematics, especially those influenced by the Indian mathematician Srinivasa Ramanujan.

## 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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## William Shanks

William Shanks (25 January 1812 – June 1882) was a British amateur mathematician.

## Zipf's law

Zipf's law is an empirical law formulated using mathematical statistics that refers to the fact that many types of data studied in the physical and social sciences can be approximated with a Zipfian distribution, one of a family of related discrete power law probability distributions.

## References

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