On an iteration leading to a q-analogue of the Digamma function
Christian Berg (University of Copenhagen), Helle Bjerg Petersen, (University of Copenhagen)
TL;DR
This paper explores the q-Digamma function within an iterative framework and identifies a related probability measure with moments that are q-analogues of harmonic number reciprocals.
Contribution
It establishes a connection between the q-Digamma function and an iteration, and determines a probability measure with moments as q-analogues of harmonic number reciprocals.
Findings
q-Digamma function appears in a specific iteration
Identified probability measure with moments as q-analogues of harmonic numbers
Provides new insights into q-analogue functions and their properties
Abstract
We show that the q-Digamma function psi_q for 0<q<1 appears in an iteration studied by Berg and Dur\'an. In addition we determine the probability measure \nu_q with moments 1/\sum_{k=1}^{n+1} (1-q)/(1-q^k), which are q-analogues of the reciprocals of the harmonic numbers.
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