Answers are grounded in this paper and cite their sources.
This analysis evaluates the Mellin transform of various trigonometric functions, highlighting implications for integral techniques.
In this paper, we focus on calculating the Mellin transform of three types of trigonometric functions, namely, \(∑ₖ₌₀ⁿcₖsin(aₖx)\), \(∑ₖ₌₀ⁿcₖcos(aₖx)\) and \(∑ₖ₌₁ⁿcₖ(1-cos(aₖx))\), where \(n\) is an integer, \(cₖ*\) and \(0<a₀<⋯<aₙ\). Our approach is based on the application of techniques from linear algebra, calculus, Laplace transform, and special functions. In particular, we give an evaluation of the integral \(∫₀∞{sinⁿx}{xα}dx\), \(n*\), \(0<α<n+1\).
No takes yet. Share an insight, caveat, or question.
Mâagli et al. (2025) studied this question.
Synapse has enriched 10 related papers. Consider them for comparative context: