A Note on an Arctangent Integral by Fritz Oberhettinger

HAL (Le Centre pour la Communication Scientifique Directe) 2026 Preprint Open access

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Authors: Robert G. Reynolds
DOI: 10.71712/317q-8c20
Cited by: 0

Abstract

An exact expression for an Arctangent definite integral is derived and evaluated using contour integration. A new closed form expression for this definite integral is given in terms of the Hurwitz-Lerch zeta function. Special cases of this definite are evaluated in terms of special functions and fundamental constants. A short table summarizing interesting results is produced.

Fields of Study & Subjects

Mathematics and Applications History and Theory of Mathematics

Publication details

Journal / source
HAL (Le Centre pour la Communication Scientifique Directe)
Publication date
16 June 2026
Language
EN
Document type
Preprint