Evaluation of the Improper Integrals ∫∞0(sin(βx)/x)^n dx

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Luo, Qiu-Ming and Guo, Bai-Ni (2000) Evaluation of the Improper Integrals ∫∞0(sin(βx)/x)^n dx. RGMIA research report collection, 4 (4).

Abstract

In this article, using the trigonometric power formulae, the L’Hospital rule and integration by parts, some evaluations for the improper integrals ∫∞0(sin x/x)^n dx and ∫∞0(sin(βx)/x)^n dx for positive integer n ≥ 2 and β ≠ 0 are established. As by-products, three combinatorial identities are obtained.

Item type Article
URI https://vuir.vu.edu.au/id/eprint/18053
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, integration by parts, L’Hospital rule, Dirichlet integral
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