On Berndt's summation formula

2021/11/11 by Alexander E. Patkowski, Patkowski, Alexander E.
Mathematics · Medicine · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Calculus (dental) #Mathematical analysis #Mathematics #Medicine #Poisson distribution #Poisson summation formula #Statistics #Summation by parts #math.NT

paper · pdf · doi:10.48550/arxiv.2111.06256

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2021/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We offer a proof of a summation formula equivalent to one due to Berndt. Our proof uses the Muntz formula and the Poisson summation formula. By utilizing known properties of Mellin inversion, we give an example from a discontinuous function. Several new applications are offered as corollaries.

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