Abstract
We define a generalized Euler gamma function Λβ(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 Λβ(z) and its asymptotic expansion for large values of the argument.
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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 39, No. 2, pp. 87–91, 2005
Original Russian Text Copyright © by M. Spreafico
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Spreafico, M. A Generalization of the Euler Gamma Function. Funct Anal Its Appl 39, 156–159 (2005). https://doi.org/10.1007/s10688-005-0031-7
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DOI: https://doi.org/10.1007/s10688-005-0031-7