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Appendix

  • Claus Müller
Part of the Applied Mathematical Sciences book series (AMS, volume 129)

Abstract

For x ∈ ℝ+ the Г-function is defined as
$$ \Gamma (x): = \int_0^\infty {t^{x - 1} e^{ - t} dt} $$
(§35.1)
and we find for the derivatives (k ∈ ℕ)
$$ {{\left( {\frac{d}{{dx}}} \right)}^{k}}\Gamma (x) = \smallint _{0}^{\infty }{{(\ln t)}^{k}}{{t}^{{x - 1}}}{{e}^{{ - t}}}dt$$
(§35.2)
because differentiation and integration may be interchanged.

Keywords

Power Series Holomorphic Function Meromorphic Function Hypergeometric Function Taylor Approximation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Claus Müller
    • 1
  1. 1.AachenGermany

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