Supercongruences for the Catalan-Larcombe-French numbers
From MaRDI portal
Publication:5962077
DOI10.1007/s11139-009-9218-5zbMath1218.11025arXiv0905.4187OpenAlexW2076539023WikidataQ60692023 ScholiaQ60692023MaRDI QIDQ5962077
Frazer Jarvis, Helena A. Verrill
Publication date: 16 September 2010
Published in: The Ramanujan Journal (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0905.4187
recurrence relationbinomial coefficientPicard-Fuchs equationCatalan-Larcombe-French numbersFranel numberssupercongruences
Factorials, binomial coefficients, combinatorial functions (05A10) Binomial coefficients; factorials; (q)-identities (11B65) Fourier coefficients of automorphic forms (11F30) Special sequences and polynomials (11B83) Elliptic functions and integrals (33E05)
Related Items
Proof of two conjectural supercongruences involving Catalan-Larcombe-French numbers, Sun's log-concavity conjecture on the Catalan-Larcombe-French sequence, Congruences involving \(g_n(x)=\sum\limits_{k=0}^n\dbinom{n}{k}^2\dbinom{2k}{k}x^k\), Super congruences for two Apéry-like sequences, Proof of a supercongruence conjectured by Z.-H. Sun, Congruences for Franel numbers, Congruences for sums involving Franel numbers, Two-log-convexity of the Catalan-Larcombe-French sequence, New series for powers of \(\pi\) and related congruences, A supercongruence for generalized Domb numbers, On two congruences involving Franel numbers, On two congruences involving Apéry and Franel numbers, Identities and congruences for Catalan–Larcombe–French numbers, Modular forms, hypergeometric functions and congruences, Proof of three divisibilities of Franel numbers and binomial coefficients, THE LOG-BEHAVIOR OF THE CATALAN–LARCOMBE–FRENCH SEQUENCE, Log-behavior of two sequences related to the elliptic integrals, On two congruence conjectures, Congruences via modular forms, Some congruences on \(q\)-Franel numbers and \(q\)-Catalan numbers, CONGRUENCES AMONG POWER SERIES COEFFICIENTS OF MODULAR FORMS, Proof of two conjectures of Sun on congruences for Franel numbers, Some congruences involving powers of Legendre polynomials, Ramanujan-type supercongruences involving Almkvist-Zudilin numbers
Uses Software
Cites Work
- Another congruence for the Apéry numbers
- Recurrences for sums of powers of binomial coefficients
- Modular Forms on Noncongruence Subgroups and Atkin–Swinnerton-Dyer Relations
- Monstrous Moonshine
- Multiplicative 𝜂-quotients
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
