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Gamma and Beta Function Integrals
2014In 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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Ramanujan's Extensions of the Gamma and Beta Functions
The American Mathematical Monthly, 1980(1980). Ramanujan's Extensions of the Gamma and Beta Functions. The American Mathematical Monthly: Vol. 87, No. 5, pp. 346-359.
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Relation Between the Beta and the Gamma Functions
Mathematics Magazine, 1968(1968). Relation Between the Beta and the Gamma Functions. Mathematics Magazine: Vol. 41, No. 1, pp. 37-39.
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Analytic Subtraction Applied to the Incomplete Gamma and Beta Functions
SIAM Journal on Scientific and Statistical Computing, 1980The purpose of this paper is to draw attention to a method of performing analytic subtractions that can dramatically improve the numerical stability of a continued fraction (cf) or series expansion. The method is applied to the computation of the incomplete gamma and beta functions.
G. W. Walster, Marietta J. Tretter
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The Gamma, Beta, Pi, and Psi Functions
1995Publisher Summary This chapter discusses the gamma, beta, pi, and psi functions. The gamma function, denoted by Γ(x), provides a generalization of n factorial n to the case in which n is not an integer. It is defined by the Euler integral. The chapter presents the special function of Γ(x) and the gamma function in the complex plane.
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Stereoselective Access to Functionalized .beta±gamma. Unsaturated Acids.
ChemInform, 2003AbstractFor Abstract see ChemInform Abstract in Full Text.
Mohamed Abarbri +3 more
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Computation of bivariate gamma and inverted beta distribution functions
Journal of Statistical Computation and Simulation, 1995This paper considers the evaluation of the distribution functions of the bivariate gamma distribution of Wicksell and Kibble, and a bivariate inverted beta distribution. Simple expansions of the distribution functions in terms of marginal quantities and the negative binomial probabilities are derived.
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Functions of Beta- and Gamma-Catenins in Prostate Cancer
2001Abstract : Contact among cells in epithelia plays an important role in regulating cell growth and migration. Cell-cell contact generally suppresses cell division and limits migration, while disruption of cell-cell interactions stimulates cell cycle entry and permits migration.
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