On an iteration leading to a q-analogue of the Digamma function
Classical Analysis and ODEs
2017-01-30 v1
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.
Cite
@article{arxiv.1111.0250,
title = {On an iteration leading to a q-analogue of the Digamma function},
author = {Christian Berg and Helle Bjerg Petersen},
journal= {arXiv preprint arXiv:1111.0250},
year = {2017}
}
Comments
12 pages, 2 figures