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Extended de Montmort-Prudnikov Sum

Author

Listed:
  • 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)

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.

Suggested Citation

  • Robert Reynolds & Allan Stauffer, 2023. "Extended de Montmort-Prudnikov Sum," Mathematics, MDPI, vol. 11(2), pages 1-8, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:333-:d:1029317
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