Transcendental values of the incomplete gamma function and related questions

  title={Transcendental values of the incomplete gamma function and related questions},
  author={M. Murty and Ekata Saha},
  journal={Archiv der Mathematik},
For s, x > 0, the lower incomplete gamma function is defined to be the integral $${\gamma(s,x):=\int_{0}^{x} t^{s} e^{-t} \frac{dt}{t}}$$γ(s,x):=∫0xtse-tdtt, which can be continued analytically to an open subset of $${\mathbb{C}^{2}}$$C2. 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… Expand
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