New analogues of Clausen's identities arising from the theory of modular forms

DOI10.1016/j.aim.2011.06.011zbMath1234.33009OpenAlexW2007690212WikidataQ60692098 ScholiaQ60692098MaRDI QIDQ639552

Heng Huat Chan, Wadim Zudilin, Yoshio Tanigawa, Yifan Yang

Publication date: 22 September 2011

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

Full work available at URL: https://doi.org/10.1016/j.aim.2011.06.011

zbMATH Keywords

Clausen-type identitiesmodular forms and functionsRamanujan-type series for 1/pi

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Modular and automorphic functions (11F03) Holomorphic modular forms of integral weight (11F11) Generalized hypergeometric series, ({}_pF_q) (33C20) Evaluation of number-theoretic constants (11Y60)

Related Items (24)

Mosaic Supercongruences of Ramanujan Type ⋮ Rational analogues of Ramanujan's series for 1/π ⋮ A \(q\)-Clausen-Orr type formula and its applications ⋮ Ramanujan-type identities for Shimura curves ⋮ Super congruences for two Apéry-like sequences ⋮ Generating functions of Legendre polynomials: a tribute to Fred Brafman ⋮ Level 17 Ramanujan-Sato series ⋮ Sporadic sequences, modular forms and new series for \(1/\pi\) ⋮ Infinitely log-monotonic combinatorial sequences ⋮ The Bailey-Brafman identity and its analogues ⋮ New Representations for all Sporadic Apéry-Like Sequences, With Applications to Congruences ⋮ Congruences for sums involving Franel numbers ⋮ Polynomial reduction for holonomic sequences and applications in \(\pi\)-series and congruences ⋮ New series for powers of \(\pi\) and related congruences ⋮ On three conjectural congruences of Z.-H. Sun involving Apéry and Apéry-like numbers ⋮ Identities and congruences for Catalan–Larcombe–French numbers ⋮ Arithmetic properties of Picard-Fuchs equations and holonomic recurrences ⋮ A GENERATING FUNCTION OF THE SQUARES OF LEGENDRE POLYNOMIALS ⋮ Supercongruences for sums involving Domb numbers ⋮ HYPERGEOMETRIC MODULAR EQUATIONS ⋮ Generating functions of Legendre polynomials: A tribute to Fred Brafman ⋮ A generalization of a Brafman-Bailey type identity ⋮ Higher order Turán inequalities for combinatorial sequences ⋮ Ramanujan-type \(1/\pi\)-series from bimodular forms

Uses Software

• OEIS

Cites Work

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• The Apéry numbers, the Almkvist-Zudilin numbers and new series for \(1/\pi\)
• New \(_{5}F_{4}\) hypergeometric transformations, three-variable Mahler measures, and formulas for \(1/ \pi \)
• Congruence properties of Apéry numbers
• Some congruences for Apery numbers
• Ramanujan's modular equations and Atkin-Lehner involutions
• Binomial identities -- combinatorial and algorithmic aspects
• On differential equations satisfied by modular forms
• Domb's numbers and Ramanujan-Sato type series for \(1/\pi\)
• Generalizations of Clausen's Formula and algebraic transformations of Calabi–Yau differential equations
• CONGRUENCES RELATED TO MODULAR FORMS
• NEW REPRESENTATIONS FOR APÉRY‐LIKE SEQUENCES
• Ramanujan's cubic continued fraction revisited
• Monodromy of Picard-Fuchs differential equations for Calabi-Yau threefolds
• CONGRUENCES SATISFIED BY APÉRY-LIKE NUMBERS

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