q-Analogues of two "divergent" Ramanujan-type supercongruences

Victor J. W. Guo

q-Analogues of two "divergent" Ramanujan-type supercongruences

Number Theory 2018-02-06 v1 Combinatorics

Authors: Victor J. W. Guo

Abstract

Guillera and Zudilin proved three "divergent" Ramanujan-type supercongruences by means of the Wilf-Zeilberger algorithmic technique. In this paper, we prove $q$ -analogues of two of them via the $q$ -WZ method. Additionally, we give $q$ -analogues of two related congruence of Sun, one is confirmed and the other is conjectural.

Keywords

q-analogues supercongruences ramanujan-type q-WZ method wilf-zeilberger congruences

Cite

@article{arxiv.1802.01260,
  title  = {q-Analogues of two "divergent" Ramanujan-type supercongruences},
  author = {Victor J. W. Guo},
  journal= {arXiv preprint arXiv:1802.01260},
  year   = {2018}
}

Comments

18 pages

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