Evaluations of the improper integrals ∫ 0 ∞ [sin 2m (αx)]/(x 2n)] cos(bx) dx and ∫ 0 ∞ [sin 2m+1 (αx)]/(x 2n+1 )] cos(bx)dx

Luo, Qiu-Ming and Qi, Feng (2002) Evaluations of the improper integrals ∫ 0 ∞ [sin 2m (αx)]/(x 2n)] cos(bx) dx and ∫ 0 ∞ [sin 2m+1 (αx)]/(x 2n+1 )] cos(bx)dx. RGMIA research report collection, 6 (1).

Abstract

In this article, using L’Hospital rule, mathematical induction, the trigonometric power formulae and integration by parts, some integral formulae for improper integrals ∫ 0 ∞ [sin 2m (αx)]/(x 2n)] cos(bx) dx and ∫ 0 ∞ [sin 2m+1 (αx)]/(x 2n+1 )] cos(bx)dx are established, where m ≥ n are all positive integers and real numbers α ≠ 0 and b ≥ 0.

Item type Article
URI http://vuir.vu.edu.au/id/eprint/17797
Subjects Current > FOR Classification > 0102 Applied Mathematics
Current > FOR Classification > 0103 Numerical and Computational Mathematics
Current > Collections > Research Group in Mathematical Inequalities and Applications (RGMIA)
Keywords evaluation, improper integral, integral formula, inequality, integration by parts, L’Hospital rule, Dirichlet integral, mathematical induction
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