Balanced polygamma function について

Words near each other

Dictionary Lists

mini英和辞書

翻訳と辞書　辞書検索 [ 開発暫定版 ]

スポンサードリンク

Generalized polygamma function ：ウィキペディア英語版

Balanced polygamma function
In mathematics, the generalized polygamma function or balanced negapolygamma function is a function introduced by Olivier Espinosa Aldunate and Victor H. Moll.〔(Olivier Espinosa Victor H. Moll. A Generalized polygamma function. Integral Transforms and Special Functions Vol. 15, No. 2, April 2004, pp. 101–115 )〕
It generalizes the polygamma function to negative and fractional order, but remains equal to it for integer positive orders.
==Definition==

The generalized polygamma function is defined as follows:
:

\psi(z,q)=\frac \,

or alternatively,
:

\psi(z,q)=e^\frac\left(e^\frac\right),

where

\psi(z)

\zeta(z,q),

is the Hurwitz zeta function.
The function is balanced, in that it satisfies the conditions

f(0)=f(1)

and

\int_0^1 f(x) dx = 0

翻訳と辞書 : 翻訳のためのインターネットリソース