A new \(q\)-extension of the (H.2) congruence of Van Hamme for primes \(p\equiv 1\pmod{4}\)

DOI10.1007/s00025-021-01517-zzbMath1496.11033OpenAlexW3201996748MaRDI QIDQ2242449

Yanyan Li

Publication date: 9 November 2021

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00025-021-01517-z

zbMATH Keywords

cyclotomic polynomialsharmonic numbersPochhammer symbolgamma functions\(q\)-congruences

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Binomial coefficients; factorials; (q)-identities (11B65) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Congruences; primitive roots; residue systems (11A07) Special functions in characteristic (p) (gamma functions, etc.) (33E50)

Related Items (8)

A new extension of the (A.2) supercongruence of Van Hamme ⋮ Further \(q\)-supercongruences from a transformation of Rahman ⋮ Three families of \(q\)-supercongruences from a quadratic transformation of Rahman ⋮ A new extension of Van Hamme's (E.2) supercongruence ⋮ A new \(q\)-variation of the (C.2) supercongruence of Van Hamme ⋮ Two \(q\)-congruences involving double basic hypergeometric sums ⋮ \(q\)-supercongruences on triple and quadruple sums ⋮ A -SUPERCONGRUENCE MODULO THE THIRD POWER OF A CYCLOTOMIC POLYNOMIAL

Uses Software

• SIGMA

Cites Work

• On the supercongruence conjectures of van Hamme
• On sums of Apéry polynomials and related congruences
• Generalized Legendre polynomials and related supercongruences
• A family of \(q\)-congruences modulo the square of a cyclotomic polynomial
• Some supercongruences occurring in truncated hypergeometric series
• On Van Hamme's (A.2) and (H.2) supercongruences
• A further \(q\)-analogue of Van Hamme's (H.2) supercongruence for any prime \(p\equiv 1\pmod{4}\)
• Another family of \(q\)-congruences modulo the square of a cyclotomic polynomial
• Supercongruences concerning truncated hypergeometric series
• A new extension of the (H.2) supercongruence of Van Hamme for primes \(p\equiv 3\operatorname{mod}{4}\)
• A family of \(q\)-hypergeometric congruences modulo the fourth power of a cyclotomic polynomial
• On a \(q\)-deformation of modular forms
• Symbolic summation assists combinatorics
• Some q-supercongruences for truncated basic hypergeometric series
• On sums involving products of three binomial coefficients
• A further q-analogue of Van Hamme’s (H.2) supercongruence for primes p ≡ 3(mod4)
• Some supercongruences on truncated hypergeometric series
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