Abstract
For s, x > 0, the lower incomplete gamma function is defined to be the integral \({\gamma(s,x):=\int_{0}^{x} t^{s} e^{-t} \frac{dt}{t}}\), which can be continued analytically to an open subset of \({\mathbb{C}^{2}}\). Here in this article, we study the transcendence of special values of the lower incomplete gamma function, by means of transcendence of certain infinite series. These series are variants of series which are of great interest in number theory. However, these series are also of independent interest and can be studied in the context of the theory of E-functions.
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M. Ram Murty’s research was partially supported by an NSERC Discovery grant. Ekata Saha’s research was supported by an IMSc PhD Fellowship.
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Murty, M.R., Saha, E. Transcendental values of the incomplete gamma function and related questions. Arch. Math. 105, 271–283 (2015). https://doi.org/10.1007/s00013-015-0800-3
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DOI: https://doi.org/10.1007/s00013-015-0800-3