Generalizations of the (F.2) supercongruence of Van Hamme
DOI10.1007/s13398-023-01532-5OpenAlexW4389195281MaRDI QIDQ6144657
Publication date: 29 January 2024
Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s13398-023-01532-5
supercongruence\(q\)-supercongruencecreative microscoping methodJackson's \(_6\phi_5\) summation formula
Binomial coefficients; factorials; (q)-identities (11B65) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Congruences; primitive roots; residue systems (11A07) Evaluation of number-theoretic constants (11Y60)
Cites Work
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- A \(q\)-microscope for supercongruences
- Super congruences and Euler numbers
- Proof of a \(q\)-supercongruence conjectured by Guo and Schlosser
- Some \(q\)-supercongruences modulo the fourth power of a cyclotomic polynomial
- Factors of certain sums involving central \(q\)-binomial coefficients
- A \(q\)-supercongruence from a \(q\)-analogue of Whipple's \({}_3F_2\) summation formula
- A new extension of the (A.2) supercongruence of Van Hamme
- A variation of the \(q\)-Wolstenholme theorem
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- Dwork-type supercongruences through a creative \(q\)-microscope
- Two \(q\)-supercongruences from Watson's transformation
- \(q\)-analogues of the (E.2) and (F.2) supercongruences of van Hamme
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- \(q\)-supercongruences from squares of basic hypergeometric series
- Further generalizations of four supercongruences of Rodriguez-Villegas
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