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Generalization of Certain Hyperbolic Integrals and a Dilogarithm Functional Relation

Generalization of Certain Hyperbolic Integrals and a Dilogarithm Functional Relation

Year:    2024

Author:    F. M. S. Lima

Analysis in Theory and Applications, Vol. 40 (2024), Iss. 4 : pp. 422–434

Abstract

In a previous work [Indag. Math., 23(1) (2012)], I did employ a hyperbolic version of the Beukers, Calabi, and Kolk change of variables to solve 1010(1x2y2)1dxdy, which yielded exact closed-form expressions for some definite integrals and, from one of them, I proved a two-term dilogarithm identity. Here in this note, I derive closed-form expressions for b0[sinh1(cosh x)x]dx,b0 and β/2α/2ln(tanh x)dx,  bR, where α:=sinh1(1) and β:=b+sinh1(cosh b). From these general results, I derive a dilogarithm functional relation.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ata.OA-2018-0011

Analysis in Theory and Applications, Vol. 40 (2024), Iss. 4 : pp. 422–434

Published online:    2024-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    13

Keywords:    Degenerate nonlinear elliptic equation Weighted Sobolev spaces. Hyperbolic integrals dilogarithm function dilogarithm relations.

Author Details

F. M. S. Lima