Mosaic supercongruences of Ramanujan-type

TL;DR

This paper extends the known supercongruences of Ramanujan-type to include series with square roots in the summation, providing new patterns and supporting examples.

Contribution

It introduces a generalization of Ramanujan-type supercongruences to series involving square roots, broadening the scope of previous observations.

Findings

Identifies new supercongruence patterns involving square roots.

Provides examples supporting the generalized supercongruences.

Extends the framework of Ramanujan-type supercongruences.

Abstract

We generalize the patterns of supercongruences of Ramanujan-type observed by L. Van Hamme and W. Zudilin to series involving simple square roots anywhere and not only in the result of the sum. To support our observations we give some examples.