Wilf-Zeilberger seeds and non-trivial hypergeometric identities

TL;DR

This paper introduces a systematic method for generating Wilf-Zeilberger pairs to prove hypergeometric identities, confirming several conjectures related to Ramanujan-type formulas and zeta values.

Contribution

It presents a new systematic approach for generating Wilf-Zeilberger pairs, enabling proof of several previously conjectured hypergeometric identities.

Findings

Proved Ramanujan-1/π^4 formulas

Confirmed 1/π^3 hypergeometric identities

Derived a series for ζ(5)

Abstract

Through a systematic approach on generating Wilf-Zeilberger-pairs, we prove some hypergeometric identities conjectures due to Z.W. Sun, J. Guillera and Y. Zhao etc., including two Ramanujan-$1/\pi^4$, one $1/\pi^3$ formulas as well as a remarkable series for $\zeta(5)$.