词条 | K-function |
释义 |
In mathematics, the K-function, typically denoted K(z), is a generalization of the hyperfactorial to complex numbers, similar to the generalization of the factorial to the Gamma function. Formally, the K-function is defined as It can also be given in closed form as where ζ'(z) denotes the derivative of the Riemann zeta function, ζ(a,z) denotes the Hurwitz zeta function and Another expression using polygamma function is[1] Or using balanced generalization of Polygamma function:[2] where A is Glaisher constant. The K-function is closely related to the Gamma function and the Barnes G-function; for natural numbers n, we have More prosaically, one may write The first values are 1, 4, 108, 27648, 86400000, 4031078400000, 3319766398771200000, ... ({{OEIS|A002109}}). References1. ^Victor S. Adamchik. PolyGamma Functions of Negative Order 2. ^Olivier Espinosa Victor H. Moll. A Generalized polygamma function. Integral Transforms and Special Functions Vol. 15, No. 2, April 2004, pp. 101–115 External links
1 : Gamma and related functions |
随便看 |
|
开放百科全书收录14589846条英语、德语、日语等多语种百科知识,基本涵盖了大多数领域的百科知识,是一部内容自由、开放的电子版国际百科全书。