Some Inequalities for the Ratios of Generalized Digamma Functions

TL;DR

This paper establishes new inequalities for ratios of generalized digamma functions using series representations of the $(q,k)$-digamma and $(p,q)$-digamma functions, contributing to the mathematical understanding of these special functions.

Contribution

It introduces novel inequalities for generalized digamma functions based on their series representations, expanding the theoretical framework of special functions.

Findings

Derived inequalities for ratios of generalized digamma functions.

Utilized series representations of $(q,k)$-digamma and $(p,q)$-digamma functions.

Enhanced understanding of properties of generalized digamma functions.

Abstract

Some inequalities for the ratios of generalized digamma functions are presented. The approache makes use of the series representations of the $(q,k)$-digamma and $(p,q)$-digamma functions.