"Divergent" Ramanujan-type supercongruences

TL;DR

This paper proves new supercongruences related to divergent Ramanujan-type series for 1/π and 1/π^2 using the Wilf–Zeilberger algorithm, expanding understanding of these mathematical phenomena.

Contribution

It introduces novel supercongruences associated with divergent Ramanujan-type series and demonstrates their proof using algorithmic techniques.

Findings

Proved three new supercongruences for divergent Ramanujan series

Extended supercongruence theory to divergent series cases

Applied Wilf–Zeilberger algorithm successfully in this context

Abstract

"Divergent" Ramanujan-type series for $1/\pi$ and $1/\pi^2$ provide us with new nice examples of supercongruences of the same kind as those related to the convergent cases. In this paper we manage to prove three of the supercongruences by means of the Wilf--Zeilberger algorithmic technique.