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Some properties of the \(k\)-gamma function. (English) Zbl 1290.33001

The authors study some new properties of a \(k\)-gamma function \(\Gamma_k\) \((k>0)\), introduced by R. Díaz and E. Pariguan [Divulg. Mat. 15, No. 2, 179–192 (2007; Zbl 1163.33300)]. They introduce also a \(k\)-analogue \(\zeta_k\) of Riemann’s zeta function. By applying classical inequalities or a monotonicity theorem, the analogues of certain known results for the Euler gamma function are extended to the \(k\)-case.

MSC:

33B15 Gamma, beta and polygamma functions
26A48 Monotonic functions, generalizations

Citations:

Zbl 1163.33300
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