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arXiv · 2006.09575

Lobachevsky-type Formulas via Fourier Analysis

Runze Cai·Horst Hohberger·Mian Li
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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.

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Runze Cai, Horst Hohberger, Mian Li. 2020-06-17. Lobachevsky-type Formulas via Fourier Analysis. https://arxiv.org/abs/2006.09575

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