Asymptotic and exact series representations for the incomplete Gamma function

@article{Amore2005AsymptoticAE,
  title={Asymptotic and exact series representations for the incomplete Gamma function},
  author={P. Amore},
  journal={EPL},
  year={2005},
  volume={71},
  pages={1-7}
}
  • P. Amore
  • Published 2005
  • Mathematics, Physics
  • EPL
Using a variational approach, two new series representations for the incomplete Gamma function are derived: the first is an asymptotic series, which contains and improves over the standard asymptotic expansion; the second is a uniformly convergent series, completely analytical, which can be used to obtain arbitrarily accurate estimates of Γ(a,x) for any value of a or x. Applications of these formulas are discussed. 

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