Infinite Sum of the Incomplete Gamma Function Expressed in Terms of the Hurwitz Zeta Function

Robert Reynolds and Allan Stauffer
Additional contact information
Robert Reynolds: Department of Mathematics and Statistics, York University, Toronto, ON M3J1P3, Canada
Allan Stauffer: Department of Mathematics and Statistics, York University, Toronto, ON M3J1P3, Canada

Mathematics, 2021, vol. 9, issue 16, 1-7

Abstract: We apply our simultaneous contour integral method to an infinite sum in Prudnikov et al. and use it to derive the infinite sum of the Incomplete gamma function in terms of the Hurwitz zeta function. We then evaluate this formula to derive new series in terms of special functions and fundamental constants. All the results in this work are new.

Keywords: incomplete gamma function; Hurwitz zeta function; Catalan’s constant; Euler’s constant; infinite sum; contour integral (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/16/1952/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/16/1952/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:16:p:1952-:d:615013

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().