Definite Integral of Power and Algebraic Functions in terms of the Lerch Function

Authors

DOI:

https://doi.org/10.29020/nybg.ejpam.v14i3.4017

Keywords:

Lerch function, Contour integral, fundamental constants,

Abstract

Bierens de haan (1867) evaluated a definite integral involving the cotangent function and this result was also listed in Gradshteyn and Ryzhik (2007). The objective of this present note is to use this integral along with Cauchy's integral formula to derive a definite logarithmic integral in terms of the Lerch function. We will use this integral formula to produce a table of known and new results in terms of special functions and thereby expanding the list of definite integrals in both text books.

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Published

2021-08-05

Issue

Vol. 14 No. 3: (July 2021)

Section

Nonlinear Analysis

License

Upon acceptance of an article by the journal, the author(s) accept(s) the transfer of copyright of the article to European Journal of Pure and Applied Mathematics.

European Journal of Pure and Applied Mathematics will be Copyright Holder.

How to Cite

Definite Integral of Power and Algebraic Functions in terms of the Lerch Function. (2021). European Journal of Pure and Applied Mathematics, 14(3), 980-988. https://doi.org/10.29020/nybg.ejpam.v14i3.4017