Gauss summation and Ramanujan type series for $1/{\pi}$

TL;DR

This paper derives a new four-parameter series expansion formula using gamma function properties and Gauss summation, enabling the generation of numerous Ramanujan-type series for 1/π.

Contribution

It introduces a novel four-parameter series expansion formula that generalizes Ramanujan-type series for 1/π using hypergeometric functions.

Findings

Derived a four-parameter series expansion formula.

Produced infinitely many Ramanujan-type series for 1/π.

Utilized gamma function properties and Gauss summation.

Abstract

Using some properties of the gamma function and the well-known Gauss summation formula for the classical hypergeometric series, we prove a four-parameter series expansion formula, which can produce infinitely many Ramanujan type series for $1/\pi$.