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The Ramanujan Journal

, Volume 48, Issue 3, pp 577–583 | Cite as

Some identities involving Inverse Gamma integrals

  • Juan Carlos SampedroEmail author
Article
  • 102 Downloads

Abstract

In this paper we will give some identities related with the Fransén–Robinson constant and the Inverse Gamma function. The main result is to use Riemann integration techniques to get an identity that relates the value of the integral of \(\frac{1}{\varGamma (x)}\) over \((1,\infty )\) with the value of \(\frac{1}{\varGamma (x)}\) over \((-n,-n+1)\) for \(n\in \mathbb {N}\cup \{0\}\).

Keywords

Fransén–Robinson constant Classical analysis Inverse Gamma function 

Mathematics Subject Classification

11M99 

Notes

References

  1. 1.
    Andrews, G.E., Berndt, B.C.: Ramanujan’s Lost Notebook. Springer, New York (2005)zbMATHGoogle Scholar
  2. 2.
    Fransén, A.: Accurate determination of the inverse Gamma integral. BIT 19, 137–138 (1979)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsUPV/EHU-University of Basque CountryLeioaSpain

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