Remark On Two Results due to Ramanujan on Hypergeometric Series

TL;DR

This paper examines two hypergeometric series results attributed to Ramanujan, clarifies the correctness of one, and provides corrected forms for the other, contributing to the accurate understanding of Ramanujan's work.

Contribution

It clarifies the correctness of one of Ramanujan's hypergeometric series results and offers corrected forms for the other, resolving discrepancies noted by Berndt.

Findings

One of Ramanujan's results is confirmed correct.

A corrected form of the second result is provided.

Clarifies historical discrepancies in Ramanujan's hypergeometric series results.

Abstract

During the course of verifying the results of Ramanujan on hypergeometric series, Berndt in his notebooks, Part II mentioned corrected forms of two of the Ramanujan's results. The aim of this short research note is to point out that one of the results obtained by Ramanujan is correct (and not of Berndt's result) and the second result (which is slightly differ from Ramanujan's result and Berndt's result) is given here in corrected form.