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
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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 | https://vuir.vu.edu.au/id/eprint/17797 |
| Subjects | Historical > FOR Classification > 0102 Applied Mathematics Historical > 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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