Remarkable properties of the $\text{sinc}_{p, q}$ functions and related integrals
Classical Analysis and ODEs
2021-02-05 v2
Abstract
Different types of sinc integrals are investigated when the standard sine function is replaced by the generalised in two parameters. A striking generalisation of the improper Dirichlet integral is achieved. A second surprising but interesting generalisation of the identity between the Dirichlet integral and that of the integrand is discovered. Moreover, an asymptotically sharpened form of Ball's integral inequality is obtained in terms of two parameters.
Keywords
Cite
@article{arxiv.2005.00477,
title = {Remarkable properties of the $\text{sinc}_{p, q}$ functions and related integrals},
author = {Houry Melkonian and Shingo Takeuchi},
journal= {arXiv preprint arXiv:2005.00477},
year = {2021}
}