Mathematics and Statistics Vol. 9(4), pp. 588 - 602
DOI: 10.13189/ms.2021.090418
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Derivation of Some Entries in the Tables of David Bierens De Haan and Anatolii Prudnikov: An Exercise in Integration Theory

Robert Reynolds ^*, Allan Stauffer
Department of Mathematics and Statistics, York University, Faculty of Science, Canada

ABSTRACT

It is always useful to improve the catalogue of definite integrals available in tables. In this paper we use our previous work on Lobachevsky integrals to derive entries in the tables by Bierens De Haan and Anatolli Prudnikov featuring errata results and new integral formula for interested readers. In this work we derive a definite integral given by (1) in terms of the Lerch function. The importance of this work lies in the derivation of known and new results not presently found in current literature. We used our contour integral method and applied it to an integral in Prudnikov and used it to derive a closed form solution in terms of a special function. The advantage of using a special function is the added benefit of analytic continuation which widens the range of computation of the parameters. Special functions have significance in mathematical analysis, functional analysis, geometry, physics, and other applications. Special functions are used in the solutions of differential equations or integrals of elementary functions. Special functions are linked to the theory of Lie groups and Lie algebras, as well as certain topics in mathematical physics.

KEYWORDS
Entries in Bierens De Haan, Lerch Function, Definite Integral

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Robert Reynolds , Allan Stauffer , "Derivation of Some Entries in the Tables of David Bierens De Haan and Anatolii Prudnikov: An Exercise in Integration Theory," Mathematics and Statistics, Vol. 9, No. 4, pp. 588 - 602, 2021. DOI: 10.13189/ms.2021.090418.

(b). APA Format:
Robert Reynolds , Allan Stauffer (2021). Derivation of Some Entries in the Tables of David Bierens De Haan and Anatolii Prudnikov: An Exercise in Integration Theory. Mathematics and Statistics, 9(4), 588 - 602. DOI: 10.13189/ms.2021.090418.