A functional logarithmic formula for hypergeometric functions 3F2

TL;DR

This paper establishes a sufficient condition under which the hypergeometric function 3F2 can be expressed as a linear combination of logarithmic functions, utilizing a regulator formula from prior work.

Contribution

It introduces a new sufficient condition for representing 3F2 hypergeometric functions as logarithmic combinations, based on a previously proven regulator formula.

Findings

Identifies conditions for 3F2 to be a linear combination of logarithms

Uses a regulator formula from earlier work to prove the result

Provides a theoretical framework for hypergeometric function analysis

Abstract

We give a sufficient condition for that the hypergeometric function 3F2 is a linear combination of the logarithmic function. The proof is based on the regulator formula which we proved in another preprint, arXiv:1709.04144.