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Was (wer) ist gamma function - definition
Gamma function
![[[Daniel Bernoulli]]'s letter to [[Christian Goldbach]], October 6, 1729](https://commons.wikimedia.org/wiki/Special:FilePath/DanielBernoulliLettreAGoldbach-1729-10-06.jpg?width=200 "[[Daniel Bernoulli]]'s letter to [[Christian Goldbach]], October 6, 1729")
 gamma function from -4.5-2.5i to 4.5+2.5i.svg?width=200 "reproduction of a famous complex plot by Janhke and Emde (Tables of Functions with Formulas and Curves, 4th ed., Dover, 1945) of the gamma function from -4.5-2.5i to 4.5+2.5i")
EXTENSION OF THE FACTORIAL FUNCTION, WITH ITS ARGUMENT SHIFTED DOWN BY 1, TO REAL AND COMPLEX NUMBERS
Gamma-function; Complete gamma function; Gamma Function; Gamma integral; Euler Gamma Function; Γ(x); Γ function; Raabe's formula; Approximations of the gamma function; Weierstrass definition of the gamma function; Complex number factorial
In mathematics, the gamma function (represented by , the capital letter gamma from the Greek alphabet) is one commonly used extension of the factorial function to complex numbers. The gamma function is defined for all complex numbers except the non-positive integers.
Multiple gamma function
 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg?width=200 "Plot of the Barnes G aka double gamma function G(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D")
GENERALIZATION OF THE EULER GAMMA FUNCTION AND THE BARNES G-FUNCTION
Barnes gamma function; Double gamma function; Triple gamma function; Barnes multiple gamma function; Multiple Gamma function
In mathematics, the multiple gamma function \Gamma_N is a generalization of the Euler gamma function and the Barnes G-function. The double gamma function was studied by .
Q-gamma function
Q-ANALOG OF THE GAMMA FUNCTION
Q-Gamma function; Basic gamma function; Q gamma function
In q-analog theory, the q-gamma function, or basic gamma function, is a generalization of the ordinary gamma function closely related to the double gamma function. It was introduced by .
