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 \(n\in \mathbb {N}\cup \{0\}\).
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References
Andrews, G.E., Berndt, B.C.: Ramanujan’s Lost Notebook. Springer, New York (2005)
Fransén, A.: Accurate determination of the inverse Gamma integral. BIT 19, 137–138 (1979)
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Sampedro, J.C. Some identities involving Inverse Gamma integrals. Ramanujan J 48, 577–583 (2019). https://doi.org/10.1007/s11139-018-0082-z
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DOI: https://doi.org/10.1007/s11139-018-0082-z