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Published in:
1998 | OriginalPaper | Chapter
Appendix
Author : Claus Müller
Published in: Analysis of Spherical Symmetries in Euclidean Spaces
Publisher: Springer New York
Included in: Professional Book Archive
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For x ∈ ℝ+ the Г-function is defined as (§35.1)$$ \Gamma (x): = \int_0^\infty {t^{x - 1} e^{ - t} dt} $$ and we find for the derivatives (k ∈ ℕ) (§35.2)$$ {{\left( {\frac{d}{{dx}}} \right)}^{k}}\Gamma (x) = \smallint _{0}^{\infty }{{(\ln t)}^{k}}{{t}^{{x - 1}}}{{e}^{{ - t}}}dt$$ because differentiation and integration may be interchanged.