Extended de Montmort-Prudnikov Sum

Robert Reynolds () and Allan Stauffer
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Robert Reynolds: Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada
Allan Stauffer: Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada

Mathematics, 2023, vol. 11, issue 2, 1-8

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.

Keywords: derangement polynomial; incomplete gamma function; de montmort; cauchy integral (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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