Series for $1/\pi$ arising from Cauchy product

TL;DR

This paper proves a series for 1/π conjectured by Sun using Cauchy product and hypergeometric transformations, and derives additional related series involving degree 3 polynomials.

Contribution

It introduces a new proof technique for a Sun conjecture and derives new series for 1/π involving polynomials of degree 3.

Findings

Proved a series for 1/π conjectured by Sun.

Derived two additional series involving degree 3 polynomials.

Presented a table of further identities proved by the method.

Abstract

In this note, we evaluate a series for $1/\pi$ conjectured by Sun. Our proof uses the Cauchy product and hypergeometric transformations. From this result, we derive two additional analogous series for $1/\pi$ involving polynomials of degree $3$. Further identities can be proved using our method; these are presented in a table at the end of the note.