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...
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...
Moreover, the gamma function extends to an holomorphic function in the half-plane {z∈C:Re z>0}, and is still given there by the integral formula (1). Furthermore, by Taylor expansion it has a meromorphic extension on the whole plane and has simple poles zj=−j,j=0,1,2,⋯ ...
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 inverse incomplete gamma function, and the incomplete beta...
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...
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...
摘要: 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关键词:...
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...
If Z and W are both 0, the beta function returns NaN. Data Types: single | double More About collapse all Beta Function The beta function is defined by B(z,w)=∫10tz−1(1−t)w−1dt=Γ(z)Γ(w)Γ(z+w). The Γ(z) term is the gamma function Γ(z)=∫∞0tz−1e−...
The Beta function is a function of two variables that is often found in probability theory and mathematical statistics (for example, as a normalizing constant in the probability density functions of the F distribution and of the Student's t distribution). We report here some basic facts about ...