On Ramanujan's function \(k(q)=r(q)r^{2}(q^{2})\)

DOI10.1007/s11139-009-9198-5zbMath1239.11051OpenAlexW2073629013MaRDI QIDQ969417

Shaun Cooper

Publication date: 7 May 2010

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-009-9198-5

Mathematics Subject Classification ID

Theta functions and abelian varieties (14K25) Holomorphic modular forms of integral weight (11F11) Dedekind eta function, Dedekind sums (11F20) Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.) (33D52) Elliptic functions and integrals (33E05)

Related Items (19)

On Ramanujan's incomplete elliptic integral identities ⋮ THE LEVEL 12 ANALOGUE OF RAMANUJAN’S FUNCTION ⋮ On Eisenstein series, color partition and divisor function ⋮ Ramanujan's modular equations of degree 5 ⋮ On algebraic relations for Ramanujan's functions ⋮ Analogue of Ramanujan’s function k(τ) for the cubic continued fraction ⋮ Factorizations that involve Ramanujan's function \(k(q)=r(q)r^2(q^2)\) ⋮ “cases? for φ also” a question raised by Ramanujan ⋮ Unnamed Item ⋮ Some modular relations for Ramanujan's function \(k(q)=r(q)r^2(q^2)\) ⋮ Eisenstein series and elliptic functions on \(\Gamma _{0}(10)\) ⋮ Algebraic independence of certain numbers related to modular functions ⋮ Unnamed Item ⋮ Ramanujan's function \(k(\tau)=r(\tau)r^2(2\tau)\) and its modularity ⋮ HYPERGEOMETRIC MODULAR EQUATIONS ⋮ An elementary approach to Eisenstein series identities of Huber, Schultz and Ye ⋮ Ramanujan's function \(k\), revisited ⋮ 5-dissections and sign patterns of Ramanujan's parameter and its companion ⋮ Vanishing coefficients and identities concerning Ramanujan's parameters

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