2 papers
math.CA2026
Asymptotic areas between powers of sine and cosine curves
Atiratch Laoharenoo, Chanatip Sujsuntinukul
Motivated by Dombrowski and Dresden's work in 2025, we find the exact values of the limits \[\lim_{k\to\infty}\int_0^{ÏÏ}|\sin^n(kx)-\sin^nx|dx\quad\text{and}\quad \lim_{k\to\inf…
math.GM2026
Convergence criteria for Frullani-type integrals involving differences of cosines
Atiratch Laoharenoo, Chanatip Sujsuntinukul
For and , we investigate the family of improper integrals \[\int_0^\infty\frac{(\cosαx-\cosβx)^p}{x^q}dx.\] We establish a complete classif…