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

Famous Identity 

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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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