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31 relations: Algebraic independence, Arithmetic–geometric mean, Barnes G-function, Catalan's constant, Chowla–Selberg formula, Chudnovsky brothers, Digamma function, Double factorial, Elliptic integral, Factorial, Fractional part, Fransén–Robinson constant, Gamma function, Gauss's constant, Glaisher–Kinkelin constant, Half-integer, Imaginary unit, Infinite product, Integer, Mathematics, Maxima and minima, On-Line Encyclopedia of Integer Sequences, Rate of convergence, Rational number, Reciprocal gamma function, Reflection formula, Series (mathematics), Special functions, Theta function, Transcendental number, Yuri Valentinovich Nesterenko.
Algebraic independence
In abstract algebra, a subset S of a field L is algebraically independent over a subfield K if the elements of S do not satisfy any non-trivial polynomial equation with coefficients in K. In particular, a one element set is algebraically independent over K if and only if α is transcendental over K. In general, all the elements of an algebraically independent set S over K are by necessity transcendental over K, and over all of the field extensions over K generated by the remaining elements of S.
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Arithmetic–geometric mean
In mathematics, the arithmetic–geometric mean (AGM) of two positive real numbers and is defined as follows: Call and and: \end Then define the two interdependent sequences and as \end where the square root takes the principal value.
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Barnes G-function
In mathematics, the Barnes G-function G(z) is a function that is an extension of superfactorials to the complex numbers.
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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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Chowla–Selberg formula
In mathematics, the Chowla–Selberg formula is the evaluation of a certain product of values of the Gamma function at rational values in terms of values of the Dedekind eta function at imaginary quadratic irrational numbers.
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Chudnovsky brothers
David Volfovich Chudnovsky (born 1947 in Kiev) and Gregory Volfovich Chudnovsky (born 1952 in Kiev) are American mathematicians and engineers known for their world-record mathematical calculations and developing the Chudnovsky algorithm used to calculate the digits of pi with extreme precision.
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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.
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Double factorial
In mathematics, the double factorial or semifactorial of a number (denoted by) is the product of all the integers from 1 up to that have the same parity (odd or even) as.
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Elliptic integral
In integral calculus, elliptic integrals originally arose in connection with the problem of giving the arc length of an ellipse.
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Factorial
In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example, The value of 0! is 1, according to the convention for an empty product.
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Fractional part
The fractional part or decimal part of a non‐negative real number x is the excess beyond that number's integer part.
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Fransén–Robinson constant
The Fransén–Robinson constant, sometimes denoted F, is the mathematical constant that represents the area between the graph of the reciprocal Gamma function, 1/Γ(x), and the positive x axis.
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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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Gauss's constant
In mathematics, Gauss's constant, denoted by G, is defined as the reciprocal of the arithmetic–geometric mean of 1 and the square root of 2: The constant is named after Carl Friedrich Gauss, who on May 30, 1799 discovered that so that where Β denotes the beta function.
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Glaisher–Kinkelin constant
In mathematics, the Glaisher–Kinkelin constant or Glaisher's constant, typically denoted A, is a mathematical constant, related to the K-function and the Barnes G-function.
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Half-integer
In mathematics, a half-integer is a number of the form where n is an integer.
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Imaginary unit
The imaginary unit or unit imaginary number is a solution to the quadratic equation.
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Infinite product
In mathematics, for a sequence of complex numbers a1, a2, a3,...
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Integer
An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").
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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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Maxima and minima
In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range (the local or relative extrema) or on the entire domain of a function (the global or absolute extrema).
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On-Line Encyclopedia of Integer Sequences
The On-Line Encyclopedia of Integer Sequences (OEIS), also cited simply as Sloane's, is an online database of integer sequences.
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Rate of convergence
In numerical analysis, the speed at which a convergent sequence approaches its limit is called the rate of convergence.
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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.
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Reciprocal gamma function
In mathematics, the reciprocal gamma function is the function where denotes the gamma function.
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Reflection formula
In mathematics, a reflection formula or reflection relation for a function f is a relationship between f(a − x) and f(x).
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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.
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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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Theta function
In mathematics, theta functions are special functions of several complex variables.
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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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Yuri Valentinovich Nesterenko
Yuri Valentinovich Nesterenko (Ю́рий Валенти́нович Нестере́нко; born December 5, 1946 in Kharkiv, USSR now Ukraine) is a Soviet and Russian mathematician who has written papers in algebraic independence theory and transcendental number theory.
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Particular values of the Gamma function.
References
[1] https://en.wikipedia.org/wiki/Particular_values_of_the_gamma_function
