On supercongruences for truncated sums of squares of basic hypergeometric series

TL;DR

This paper extends recent supercongruences for truncated basic hypergeometric series to include their squares, revealing new congruence properties for these sums.

Contribution

It introduces novel supercongruences for the truncated sums of squares of basic hypergeometric series, expanding previous results.

Findings

Extended supercongruences to squares of series

Established new congruence relations for truncated sums

Enhanced understanding of hypergeometric series congruences

Abstract

Congruences of truncated sums of infinite series do not directly extend to congruences of the truncated sums of higher powers of these infinite series. Guo and Zudilin recently established a variety of supercongruences for truncated sums of certain basic hypergeometric series. In this note we extend some of these supercongruences to the truncated sums of the squares of the corresponding series.