A. Gamma Function Fors>0define(1)Γ(s)=∫0∞ts−1e−tdt. Γis called thegamma function. Moreover, the gamma function extends to an holomorphic function in the half-plane{z∈C:Rez>0}, and is still given there b
Riemann zeta function 的一个基本的积分表示其核心就是Gamma函数。而许多zeta函数的推广都离不开Gamma函...
Gauss 超几何级数的积分表示便是借助了Beta积分。而Mellin-Barnes积分表示则是借助了Gamma函数的性质，这...
Gauss 超几何级数的积分表示便是借助了Beta积分。而Mellin-Barnes积分表示则是借助了Gamma函数的性质，这...
Beta functionLegendre duplication formulaGauss multiplication formulaWinckler theoremStirling theoremHankel integral theoremHankel contourLogarithmic derivativeIn this chapter, we introduce the definitions and theorems for the Euler gamma function, Pochhammer symbols, and Euler beta function. We present the ...
gammafunction,beta function and their relations.Key words:Gamma function;Beta function;Wallis integral formula;advanced mathematics1 预备知识开展对 Gamma 函数和 Beta 函数等特殊函数的应用研究一直深受国内外学者的重视,如:文献[1]研究了 Gamma 函数的近似解;文献[2]研究了 Beta 随机变量函数的协方差矩阵的上...
组合恒等式Based on the theorem 1, series of combinatorial identities are derived by using the properties and relationship of Beta function and Gamma function.% 以定理1为基础,用 Beta 函数和 Gamma 函数性质及其之间的关系,导出了一系列组合恒等式张秦新乡学院...
The beta function is defined by B(z,w)=∫10tz−1(1−t)w−1dt=Γ(z)Γ(w)Γ(z+w). TheΓ(z)term is the gamma function Γ(z)=∫∞0tz−1e−tdt. References [1] Olver, F. W. J., A. B. Olde Daalhuis, D. W. Lozier, B. I. Schneider, R. F. Boisvert, C. ...
Key Words:Beta function; Psi function; Gamma function Beta函数和Gamma函数是特殊函数中十分重要的两种函数,在许多领域具有重要的作用。由于Beta函数和Gamma函数有多种形式的积分表示，Beta函数与Gamma 函数有着密切联系,Beta函数和Gamma函数在定积分、广义积分的计算上具有重要的应用。1 Beta函数及其偏导数 Beta函数...
is the Gamma function and is the Beta function. Solution Exercise 2 Compute the following ratio where is the Beta function. Solution Exercise 3 Compute the following integral: Solution How to cite Please cite as: Taboga, Marco (2021). "Beta function", Lectures on probability theory and mathema...