Surprising identities for the hypergeometric 4F3 function

TL;DR

This paper introduces a convolution method for explicitly computing certain hypergeometric 4F3 function values and explores how the dilogarithm reflection formula relates to these values, revealing they can sometimes be expressed as combinations of squared arctangent and logarithm.

Contribution

It presents a novel convolution approach for explicit 4F3 hypergeometric function evaluation and uncovers new identities involving dilogarithm reflection formulas.

Findings

Explicit computation of 4F3 values using convolution

Identification of identities involving arctangent and logarithm

Connection between dilogarithm reflection and hypergeometric values

Abstract

A convolution approach leading to an explicit computation of a value of a 4F3 function is outlined. We also investigate about the role of the dilogarithm reflection formula, leading to a remarkable consequence: in some cases, values of 4F3 are given by linear combinations of a squared arctangent and a squared logarithm.