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Analysis

International mathematical journal of analysis and its applications


CiteScore 2018: 0.72

SCImago Journal Rank (SJR) 2018: 0.363
Source Normalized Impact per Paper (SNIP) 2018: 0.530

Mathematical Citation Quotient (MCQ) 2018: 0.36

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2196-6753
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Volume 36, Issue 2

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On Volterra functions and Ramanujan integrals

Roberto Garrappa / Francesco Mainardi
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  • Department of Physics and Astronomy, University of Bologna, Via Irnerio 46, 40126 Bologna, Italy
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Published Online: 2015-09-03 | DOI: https://doi.org/10.1515/anly-2015-5009

Abstract

Volterra functions were introduced at the beginning of the twentieth century as solutions of some integral equations of convolution type with logarithmic kernel. Since then, few authors have studied this family of functions and faced with the problem of providing a clear understanding of their asymptotic behavior for small and large arguments. This paper reviews some of the most important results on Volterra functions and in particular collects, into a quite general framework, several results on their asymptotic expansions; these results turn out to be useful not only for the full understanding of the behavior of the Volterra functions but also for their numerical computation. The connections with integrals of Ramanujan type, which have several important applications, are also discussed.

Keywords: Volterra functions; Ramanujan integrals; asymptotic expansion; Laplace transform

MSC: 33E20; 45D05; 33E50; 33F05; 65D20

About the article

Received: 2015-06-20

Accepted: 2015-08-05

Published Online: 2015-09-03

Published in Print: 2016-05-01


Citation Information: Analysis, Volume 36, Issue 2, Pages 89–105, ISSN (Online) 2196-6753, ISSN (Print) 0174-4747, DOI: https://doi.org/10.1515/anly-2015-5009.

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