The q-analogue of Hölder's theorem for the gamma function
type: Item
instance of: scholarly article
title: The q-analogue of Hölder's theorem for the gamma function
zbMATH Open document ID: 0545.33004
author: P. I. Pastro
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1983-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/107921
review text: The basic gamma function \(\Gamma_ q(x)\) satisfies the recurrence relation \(\Gamma_ q(x+1)(1-q)=\Gamma_ q(x)(1-q^ x).\) By considering the logarithmic derivative of the basic gamma function g(x) which satisfies the recurrence relation \(g(x+1)=g(x)(q^ x\ln q)/(1-q^ x),\) it is shown that g(x) cannot satisfy any algebraic differential equation of finite order. This same result also applies to the basic gamma function itself which establishes the required basic analogue of Hölder's theorem.
Mathematics Subject Classification ID: 33B15
Mathematics Subject Classification ID: 33E99
zbMATH DE Number: 3867724
zbMATH Keywords: basic gamma function
reviewed by: H. Exton
MaRDI profile type: Publication
cites work: ON BASIC DOUBLE HYPERGEOMETRIC FUNCTIONS
cites work: Theq-Gamma andq-Beta Functions†
cites work: Ramanujan's Extensions of the Gamma and Beta Functions
cites work: The \(q\)-gamma function for \(q>1\)
description: scientific article; zbMATH DE number 3867724