Some truncated identities of Gauss

TL;DR

This paper derives new truncated identities for Gauss' triangular series by leveraging summation formulas, expanding understanding of partial sums and connecting previous mathematical works.

Contribution

It introduces three novel expansions for partial sums of Gauss' triangular series using summation formulas from Zhi-Guo Liu's work.

Findings

Three new expansions for partial sums of Gauss' triangular series

Connections established with previous works of Andrews-Merca and Guo-Zeng

Enhanced understanding of truncated identities in q-series

Abstract

Motivated by the works of Andrews-Merca and Guo-Zeng, we establish some truncated identities of Gauss by using some summation formulas from the works of Zhi-Guo Liu. These give three new expansions for partial sums of Gauss' triangular series.