# Some *q*-supercongruences from transformation formulas for basic hypergeometric series

### (46 pages)

**Abstract.**
Several new *q*-supercongruences are obtained using transformation
formulas for basic hypergeometric series, together with various
techniques such as suitably combining terms, and creative
microscoping, a method recently developed by the first author in
collaboration with Wadim Zudilin. More concretely, the results in
this paper include *q*-analogues of supercongruences (referring to
*p*-adic identities remaining valid for some higher power of *p*)
established by Long, by Long and Ramakrishna, and several other
*q*-supercongruences. The six basic hypergeometric transformation
formulas which are made use of are Watson's transformation, a
quadratic transformation of Rahman, a cubic transformation of Gasper
and Rahman, a quartic transformation of Gasper and Rahman, a double
series transformation of Ismail, Rahman and Suslov, and a new
transformation formula for a nonterminating very-well-poised
_{12}φ_{11} series. Also, the nonterminating
*q*-Dixon summation formula is used. A special case of the new
_{12}φ_{11} transformation formula is further utilized to
obtain a generalization of Rogers' linearization formula for the
continuous *q*-ultraspherical polynomials.

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