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On some definite integrals containing the inverse tangent function

Year: 2025

Type: article

Abstract: Evaluations are presented for definite integrals on the form \(\ [ \int_{0}^{\infty} \arctan\left(\frac{2rx}{b{2}+x{2}}\right)f(ax) dx ,]\) for numerous functions \(\ f\) subject to appropriate restrictions on the real numbers \(\ a, r\) and \(\ b\). Many new results pertaining to the particular inverse tangent function appearing in the integrand not found in the tables of Gradshteyn and Ryzhik are given.

Source: Scientia Series A: Mathematical Sciences

DOI: 10.71712/q65b-6t96

Author: Stewart, Seán M.

Institution: King Abdullah University of Science and Technology

Language: English

Topic: Advanced Mathematical Identities

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W7077514019

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