A novel kind of beta logarithmic function and their properties

Abstract

The main objective is to introduce a novel kind of beta function known as the beta logarithmic function using extended beta functions and logarithmic mean. Further, we study its essential properties and investigate various formulas of beta logarithmic functions such as integral representation, summation formula, transform formula and their statistical properties. Based on this concept, we introduce new hypergeometric and confluent hypergeometric functions and study their properties.