Geodesic
A Generalization of the Euler Gamma Function
Funkcionalʹnyj analiz i ego priloženiâ, Tome 39 (2005) no. 2, pp. 87-91

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We define a generalized Euler gamma function $\Gamma_\beta(z)$, where the product is taken over powers of integers rather than integers themselves. Studying the associated spectral functions and in particular the zeta function, we obtain the main properties of $\Gamma_\beta(z)$ and its asymptotic expansion for large values of the argument.
Keywords: Euler gamma function, spectral function, asymptotic expansion. 
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     author = {M. Spreafico},
     title = {A {Generalization} of the {Euler} {Gamma} {Function}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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M. Spreafico. A Generalization of the Euler Gamma Function. Funkcionalʹnyj analiz i ego priloženiâ, Tome 39 (2005) no. 2, pp. 87-91. http://geodesic.mathdoc.fr/item/FAA_2005_39_2_a10/