Self-reciprocal functions and double Mordell integrals

2021/10/27 by Martin Nicholson, Nicholson, Martin
Mathematics · Physics and Astronomy · #33E20 #Advanced Mathematical Identities #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials #Quantum Mechanics and Non-Hermitian Physics

paper · pdf · doi:10.48550/arxiv.2110.14337

openalex publication_date 2021/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The theory of self-reciprocal functions is applied to the study Mordell type integrals. We find two particular eigenfunctions of the double cosine Fourier transform and then use them to evaluate certain one- and two-dimensional Mordell type integrals in closed form. A reduction formula is given for a certain family of double Mordell integrals in terms of one-dimensional integrals.

Citations

• A Remarkable Definite Integral

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