Ramanujan-Type Series Related to Clausen's Product

TL;DR

This paper explores the evaluation of infinite series related to Clausen's product, deriving hypergeometric series expressions involving 1/π, and discusses methods for evaluating generalized hypergeometric series using experimental mathematics.

Contribution

It introduces new techniques for evaluating hypergeometric series connected to Clausen's product and provides explicit series expressions involving 1/π.

Findings

Derived hypergeometric series equal to 1/π expressions

Presented methods for evaluating generalized hypergeometric series

Connected series evaluations to Clausen's product

Abstract

Infinite series are evaluated through the manipulation of a series for $\cos(2t \sin^{-1}x)$ resulting from Clausen's Product. Hypergeometric series equal to an expression involving $\frac{1} {\pi}$ are determined. Techniques to evaluate generalized hypergeometric series are discussed through perspectives of experimental mathematics.