WZ pairs and q-analogues of Ramanujan series for 1/π

ABSTRACT

We prove q-analogues of two Ramanujan-type series for $1/\pi$ from q-analogues of ordinary WZ pairs.

KEYWORDS:

• Hypergeometric series
• WZ and q-WZ pairs
• q-identities
• supercongruences

AMS CLASSIFICATIONS:

• 11B65
• 33C20
• 33F10
• 33D15

Acknowledgments

I thank Wadim Zudilin for encourage me to introduce the extra parameter a that one needs to prove the kind of supercongruences in [5]. I am grateful to Doron Zeilberger for suggesting me a few years ago use my experience on WZ pairs for finding q-WZ pairs, and for telling me that he is happy because I am doing it now.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

Partially supported by E26_17R (Gobierno de Aragón).