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Evaluation of integrals with hypergeometric and logarithmic functions

Evaluation of integrals with hypergeometric and logarithmic functions AbstractWe provide an explicit analytical representation for a number of logarithmic integrals in terms of the Lerch transcendent function and other special functions. The integrals in question will be associated with both alternating harmonic numbers and harmonic numbers with positive terms. A few examples of integrals will be given an identity in terms of some special functions including the Riemann zeta function. In general none of these integrals can be solved by any currently available mathematical package. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Open Mathematics de Gruyter

Evaluation of integrals with hypergeometric and logarithmic functions

Open Mathematics , Volume 16 (1): 12 – Feb 19, 2018

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Publisher
de Gruyter
Copyright
© 2018 Sofo, published by De Gruyter
ISSN
2391-5455
eISSN
2391-5455
DOI
10.1515/math-2018-0008
Publisher site
See Article on Publisher Site

Abstract

AbstractWe provide an explicit analytical representation for a number of logarithmic integrals in terms of the Lerch transcendent function and other special functions. The integrals in question will be associated with both alternating harmonic numbers and harmonic numbers with positive terms. A few examples of integrals will be given an identity in terms of some special functions including the Riemann zeta function. In general none of these integrals can be solved by any currently available mathematical package.

Journal

Open Mathematicsde Gruyter

Published: Feb 19, 2018

Keywords: Polylogarithm function; Integral representation; Lerch transcendent function; Logarithmic integral; Riemann zeta function; 05A10; 05A19; 33C20; 11B65; 11B83; 11M06

References