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The Gamma Function and the Incomplete Gamma Functions

  • Markus Szymon Fraczek
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2139)

Abstract

The gamma function is defined for \(s \in \mathbb{C}\) by
$$\displaystyle{ \varGamma \left (s\right ) =\int _{ 0}^{\infty }t^{s-1}e^{-t}dt }$$

References

  1. 2.
    Abramowitz, M., Stegun, I.: Handbook of Mathematical Functions. Dover, New York (1964)zbMATHGoogle Scholar
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    Pugh, G.: An analysis of the Lanczos gamma approximation. Ph.D. thesis, University of British Columbia (2004)Google Scholar
  3. 128.
    Temme, N.M.: Computational aspects of incomplete gamma functions with large complex parameters. In: Proceedings of the Conference on Approximation and Computation: a Festschrift in Honor of Walter Gautschi, pp. 551–562. Birkhauser, Boston/Cambridge, MA (1994)Google Scholar
  4. 132.
    Winitzki, S.: Computing the incomplete Gamma function to arbitrary precision. LNCS 2667, 790–798 (2003)MathSciNetGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Markus Szymon Fraczek
    • 1
  1. 1.Mathematics InstituteUniversity of WarwickCoventryUK

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