Proof of conjectures of Sun on double basic hypergeometric sums. (English) Zbl 1533.11007
Summary: In this paper, we study some \(q\)-congruences on double basic hypergeometric sums. With the help of ‘creative microscoping’ method and several summation and transformation formulas for basic hypergeometric series, we confirmed several conjectures posed by Zhi-Wei Sun.
MSC:
| 11A07 | Congruences; primitive roots; residue systems |
| 11B65 | Binomial coefficients; factorials; \(q\)-identities |
| 33D15 | Basic hypergeometric functions in one variable, \({}_r\phi_s\) |
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