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

AMM-01-478.pdf (157kB)
Restricted to Repository staff only

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).


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
Download/View statistics View download statistics for this item

Search Google Scholar

Repository staff login