Elementary evaluation of ∫₀^∞sin^p t/t^q dt

2004/01/10 by Omran Kouba, Kouba, Omran
Mathematics · #Analytic Number Theory Research #FOS: Mathematics #General Mathematics (math.GM) #Mathematical and Theoretical Analysis #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.math/0401099

openalex publication_date 2004/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let p and q be two positive integers, the goal of this note is to demonstrate, in a very simple and elementary way without using advanced tools, a formula to express the value of the integral I(p,q)=∫₀^∞sin^p t\over t^qdt when it converges.

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