A q-analogue of the (A.2) supercongruence of Van Hamme for any prime p ≡ 3(mod4)
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Publication:3295474
DOI10.1142/S1793042120500694zbMath1469.11006MaRDI QIDQ3295474
Publication date: 10 July 2020
Published in: International Journal of Number Theory (Search for Journal in Brave)
Binomial coefficients; factorials; (q)-identities (11B65) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Congruences; primitive roots; residue systems (11A07)
Related Items (27)
A new extension of the (A.2) supercongruence of Van Hamme ⋮ Proof of two conjectures of Guo and Schlosser ⋮ Some \(q\)-supercongruences from transformation formulas for basic hypergeometric series ⋮ Some q-supercongruences related to Swisher’s (H.3) conjecture ⋮ Some \(q\)-supercongruences from Watson's \(_8\phi_7\) transformation formula ⋮ A \(q\)-analogue of the (A.2) supercongruence of Van Hamme for primes \(p\equiv 1\pmod{4} \) ⋮ \(q\)-supercongruences from gasper and Rahman's summation formula ⋮ Proof of some \(q\)-supercongruences modulo the fourth power of a cyclotomic polynomial ⋮ Some \(q\)-supercongruences from the Bailey transformation ⋮ \(q\)-supercongruences from squares of basic hypergeometric series ⋮ A new family of \(q\)-supercongruences modulo the fourth power of a cyclotomic polynomial ⋮ Some new \(q\)-congruences on double sums ⋮ Proof of a generalization of the (C.2) supercongruence of Van Hamme ⋮ \(q\)-analogues of the (G.2) supercongruence of Van Hamme ⋮ Two \(q\)-congruences involving double basic hypergeometric sums ⋮ \(q\)-analogues of two Ramanujan-type supercongruences ⋮ Some \(q\)-supercongruences modulo the fourth power of a cyclotomic polynomial ⋮ $q$-Supercongruences from the $q$-Saalschütz identity ⋮ Some \(q\)-supercongruences modulo the fifth power of a cyclotomic polynomial from squares of \(q\)-hypergeometric series ⋮ Some variations of a ‘divergent’ Ramanujan-type q-supercongruence ⋮ Some q-congruences on double basic hypergeometric sums ⋮ A further q-analogue of Van Hamme’s (H.2) supercongruence for primes p ≡ 3(mod4) ⋮ A -ANALOGUE OF A DWORK-TYPE SUPERCONGRUENCE ⋮ A $q$-congruence for a truncated $_4\varphi_3$ series ⋮ A \(q\)-supercongruence from a \(q\)-analogue of Whipple's \({}_3F_2\) summation formula ⋮ A new extension of the (H.2) supercongruence of Van Hamme for primes \(p\equiv 3\operatorname{mod}{4}\) ⋮ A NEW -ANALOGUE OF VAN HAMME’S (A.2) SUPERCONGRUENCE
Cites Work
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- \(q\)-analogs of some congruences involving Catalan numbers
- The Rodriguez-Villegas type congruences for truncated \(q\)-hypergeometric functions
- A \(p\)-adic analogue of a formula of Ramanujan
- On Van Hamme's (A.2) and (H.2) supercongruences
- A \(q\)-analogue of a Ramanujan-type supercongruence involving central binomial coefficients
- A \(q\)-microscope for supercongruences
- A common \(q\)-analogue of two supercongruences
- A family of \(q\)-hypergeometric congruences modulo the fourth power of a cyclotomic polynomial
- Some new \(q\)-congruences for truncated basic hypergeometric series: even powers
- Common \(q\)-analogues of some different supercongruences
- On a \(q\)-deformation of modular forms
- Some \(q\)-supercongruences from transformation formulas for basic hypergeometric series
- Some q-analogs of congruences for central binomial sums
- On a conjectured q-congruence of Guo and Zeng
- Some q-supercongruences for truncated basic hypergeometric series
- A $p$-adic supercongruence conjecture of van Hamme
- Supercongruences for polynomial analogs of the Apéry numbers
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