“Lerch Transcendent”的概念、定义、习题解题方法及翻译-数学辞典

单词

Lerch Transcendent

释义

Lerch Transcendent

A generalization of the Hurwitz Zeta Function and Polylogarithm function. Many sums of reciprocal Powerscan be expressed in terms of it. It is defined by

(1)

where any term with

is excluded.

The Lerch transcendent can be used to express the Dirichlet Beta Function

(2)

the integral of the Fermi-Dirac Distribution

(3)

where

is the Gamma Function, and to evaluate the Dirichlet L-Series.

See also Dirichlet Beta Function, Dirichlet L-Series, Fermi-Dirac Distribution, Hurwitz Zeta Function,Polylogarithm

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