Gamma函数和Beta函数 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 by the integral formula(1). Furthermore, by Taylor...
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 ...
dz右边就是beta functionB(-s,-t)，根据beta function的性质B(-s,-
一般而言，beta描述的是持有资产所承担的系统风险敞口这一概念。如果一项资产相对沪深300基准指数具有较高...
Beta 函数和 Gamma 函数有什么用？学会了欧拉的Gamma函数和Beta函数之后，就可以接着学欧拉的Alpha函数啦...
1.1.4 Beta Function In many cases it is more convenient to use the so-called beta function instead of a certain combination of values of the gamma function. The beta function is usually defined by (1.20)B(z,w)=∫01τz−1(1−τ)w−1dτ, (Re(z)>0, Re(w)>0). To establi...
Beta函数Gamma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...
relation of the Gamma function and the Beta function and the infinite -product representation of the Gamma function Furthermore,the proof of the n-duplication formula of the Gamma function is given Key words: Gamma function;Beta function;Legendre duplication formula ...
Koepf, W. "The Gamma Function." Ch. 1 in Hypergeometric Summation: An Algorithmic Approach to Summation and Special Function Identities. Braunschweig, Germany: Vieweg, pp. 4-10, 1998.Krantz, S. G. "The Gamma and Beta Functions." §13.1 in Handbook of Complex Variables. Boston, MA: ...
The gamma function is related to the Beta function by the formula [Math Processing Error] The derivative of the logarithm of the gamma function is called the digamma function; higher derivatives are the polygamma functions. The analog of the gamma function over a finite field or a finite ring...