Lobachevsky-type Formulas via Fourier Analysis
Classical Analysis and ODEs
2020-06-18 v1
Abstract
Recently renewed interest in the Lobachevsky-type integrals and interesting identities involving the cardinal sine motivate an extension of the classical Parseval formula involving both periodic and non-periodic functions. We develop a version of the Parseval formula that is often more practical in applications and illustrate its use by extending recent results on Lobachevsky-type integrals. Some previously known, interesting identities are re-proved in a more transparent manner and new formulas for integrals involving cardinal sine and Bessel functions are given.
Keywords
Cite
@article{arxiv.2006.09575,
title = {Lobachevsky-type Formulas via Fourier Analysis},
author = {Runze Cai and Horst Hohberger and Mian Li},
journal= {arXiv preprint arXiv:2006.09575},
year = {2020}
}
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8 pages