We prove a monotonicity property of the Hurwitz zeta function which, in turn, translates into a chain of inequalities for polygamma functions of different orders. We provide a probabilistic interpretation of our result by exploiting a connection between Hurwitz zeta function and the cumulants of the beta-exponential distribution.
Arbel, J., Marchal, O., Nipoti, B. (2020). On the Hurwitz zeta function with an application to the beta-exponential distribution. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2020(1) [10.1186/s13660-020-02357-1].
On the Hurwitz zeta function with an application to the beta-exponential distribution
Nipoti, B
2020
Abstract
We prove a monotonicity property of the Hurwitz zeta function which, in turn, translates into a chain of inequalities for polygamma functions of different orders. We provide a probabilistic interpretation of our result by exploiting a connection between Hurwitz zeta function and the cumulants of the beta-exponential distribution.
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