Derivation of logarithmic integrals expressed in teams of the Hurwitz zeta function

Derivation of logarithmic integrals expressed in teams of the Hurwitz zeta function

In this paper by means of contour integration we will evaluate definite integrals of the form \begin{equation*} \int_{0}^{1}\left(\ln^k(ay)-\ln^k\left(\frac{a}{y}\right)\right)R(y)dy \end{equation*} in terms of a special function, where $R(y)$ is a general function and $k$ and $a$ are arbitrary comp...

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Bibliographic Details
Main Authors: Robert Reynolds, Allan Stauffer
Format: Article
Language:English
Published: AIMS Press 2020-09-01
Series:AIMS Mathematics
Subjects:
binet
log gamma
planck’s law
euler’s constant
catalan’s constant
logarithmic function
definite integral
hexagamma
cauchy integral
entries of gradshteyn and ryzhik
Online Access:https://www.aimspress.com/article/10.3934/math.2020463/fulltext.html

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https://www.aimspress.com/article/10.3934/math.2020463/fulltext.html

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