Extended de Montmort-Prudnikov Sum-Reference-Cited by-同舟云学术

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Extended de Montmort-Prudnikov Sum

Published:2023-01-09 Issue:2 Volume:11 Page:333
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Reynolds Robert^ORCID,Stauffer Allan^ORCID

Abstract

Using a contour integral method, the de Montmort-Prudnikov sum is extended to derive a new series representation involving the incomplete gamma function. The series is uniformly convergent and completely analytical, which can be evaluated for general complex ranges of the parameters involved. Applications and evaluations of this formula are discussed.

Funder

NSERC Canada

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2227-7390/11/2/333/pdf

Reference31 articles.

1. A Method for Evaluating Definite Integrals in Terms of Special Functions with Examples;Reynolds;Int. Math. Forum,2020

2. Some Identities Involving Derangement Polynomials and Numbers and Moments of Gamma Random Variables;Jang;J. Funct. Spaces,2020

3. Derangements and Applications;Hassani;J. Integer Seq.,2003

4. The Incomplete Gamma Functions;Ameson;Math. Gaz.,2016

5. The number of derangements of a sequence with given specification;Carlitz;Fibonacci Q.,1978

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