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Gamma Functions, Beta Functions, and Related

2021
Topics of this chapter are gamma functions, beta functions, and related functions in the complex domain. The evaluations are based on various numerical techniques in dependence of the function argument. Related functions are the Pochhammer symbol, the psi or digamma function, the incomplete gamma function and its first and second derivative, the ...
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Integral representations for the Gamma function, the Beta function, and the Double Gamma function

Integral Transforms and Special Functions, 2009
A variety of integral representations for some special functions have been developed. Here we aim at presenting certain (new or known) integral representations for , B(α, β), and by using some of the known integral representations of the Hurwitz (or generalized) Zeta function ζ(s, a).
Junesang Choi, H. M. Srivastava
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Gamma, Beta, and Error Functions

2016
The gamma function, written as G(x), was first introduced by the mathematician Leonhard Euler (1707–1783) as a general form of the factorial function x! that could be applied to complex and negative numbers. Later, Adrien-Marie Legendre (1752–1833) who provided a “duplication formula” for the G function, introduced the notation that is commonly used ...
Vasudevan Lakshminarayanan   +1 more
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Different functional forms of G-protein beta gamma-subunits, beta gamma-I and beta gamma-II, in bovine brain.

Biochimica et biophysica acta, 1993
Heterotrimeric GTP binding regulatory proteins (G proteins) are involved in the signal transduction process in cells. We have previously demonstrated that G protein (Gi/o) in bovine brain contains two subspecies of the beta gamma-subunit, beta gamma-I and beta gamma-II, with distinct gamma subunits, i.e., gamma-I and gamma-II, but identical beta ...
H, Sohma   +4 more
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Gamma and Beta Function Integrals

2014
In two letters written as 1729 turned into 1730, the great Euler created what is today called the gamma function, Γ(n), defined today in textbooks by the integral $$ \Gamma \left(\mathrm{n}\right)={\displaystyle {\int}_0^{\infty }{\mathrm{e}}^{-\mathrm{x}\ }{\mathrm{x}}^{\mathrm{n}-1}\ \mathrm{dx},}\kern1em \mathrm{n}>0. $$
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Stability of generalized gamma and beta functional equations

Aequationes mathematicae, 2000
The aim of the paper is to prove stability results for the functional equation \[ f(x+p,y+q)=\varphi(x,y)f(x,y), \tag \(*\) \] where \(f:(0,\infty)\times (0,\infty) \to \mathbb R\), \(p,q\) are fixed positive numbers and \(\varphi:(0,\infty)\times (0,\infty) \to (0,\infty)\) is a suitable function. The main results are the following.
Jun, Kil Woung   +2 more
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