The Mellin Transform of Logarithmic and Rational Quotient Function in terms of the Lerch Function

Robert Reynolds, Allan Stauffer and Barbara Martinucci

Journal of Mathematics, 2021, vol. 2021, 1-13

Abstract: Upon reading the famous book on integral transforms volume II by Erdeyli et al., we encounter a formula which we use to derive a Mellin transform given by ∫0∞xm−1logkax/β2+x2γ+xdx, where the parameters a,k,β, and γ are general complex numbers. This Mellin transform will be derived in terms of the Lerch function and is not listed in current literature to the best of our knowledge. We will use this transform to create a table of definite integrals which can be used to extend similar tables in current books featuring such formulae.

Date: 2021
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/jmath/2021/8814756.pdf (application/pdf)
http://downloads.hindawi.com/journals/jmath/2021/8814756.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:8814756

DOI: 10.1155/2021/8814756

Access Statistics for this article

More articles in Journal of Mathematics from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().