Extended de Montmort-Prudnikov Sum

Extended de Montmort-Prudnikov Sum

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. Applic...

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Veröffentlicht in:Mathematics (Basel) 2023-01, Vol.11 (2), p.333
Hauptverfasser: Reynolds, Robert, Stauffer, Allan
Format: Artikel
Sprache:eng
Schlagworte:
Black holes
cauchy integral
Cosmic rays
de montmort
derangement polynomial
Food science
Gamma function
incomplete gamma function
Integrals
String theory
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Zusammenfassung: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11020333