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 ∫10∫10(1−x2y2)−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[sinh−1(cosh x)−x]dx,b≥0 and ∫β/2α/2ln(tanh x)dx, b∈R, where α:=sinh−1(1) and β:=b+sinh−1(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.