A note on some reduction formulas for the incomplete beta function and the Lerch transcedent

TL;DR

This paper introduces new reduction formulas for the incomplete beta function and Lerch transcendent, enabling easier computation and testing of numerical algorithms, with applications to integral evaluation.

Contribution

It derives novel reduction formulas expressing these special functions in terms of elementary functions, facilitating computational and analytical tasks.

Findings

New reduction formulas for incomplete beta and Lerch transcendent

Application to calculating new integrals

Performance testing of numerical algorithms

Abstract

We derive new reduction formulas for the incomplete beta function and the Lerch transcendent in terms of elementary functions. As an application, we calculate some new integrals. Also, we use these reduction formulas to test the performance of the algorithms devoted to the numerical evaluation of the incomplete beta function.