Some theorems on the Rogers-Ramanujan continued fraction and associated theta function identities in Ramanujan's Lost Notebook

Theta series; Weil representation; theta correspondences (11F27) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Continued fractions (11A55)

Related Items (21)

On Ramanujan's incomplete elliptic integral identities ⋮ On Gosper's \(\mathit{\Pi}_q\) and Lambert series identities ⋮ On some Ramanujan identities for the ratios of eta-functions ⋮ Ramanujan's modular equations of degree 5 ⋮ Factorizations that involve Ramanujan's function \(k(q)=r(q)r^2(q^2)\) ⋮ Theorems on analogous of Ramanujan’s remarkable product of theta-function and their explicit evaluations ⋮ Some modular relation on analogous of Ramanujan's remarkable product of theta-function ⋮ Some new general theorems for the explicit evaluations of the Rogers-Ramanujan continued fraction ⋮ Modular identities and explicit evaluations of a continued fraction of Ramanujan ⋮ “cases? for φ also” a question raised by Ramanujan ⋮ Parameters of Ramanujan's function \(\chi(Q)\) of degree five and their explicit evaluation ⋮ Unnamed Item ⋮ Some modular relations for Ramanujan's function \(k(q)=r(q)r^2(q^2)\) ⋮ Eisenstein series and elliptic functions on \(\Gamma _{0}(10)\) ⋮ On Ramanujan's function \(k(q)=r(q)r^{2}(q^{2})\) ⋮ Two modular equations for squares of the Rogers-Ramanujan functions with applications ⋮ A new continued fraction of Ramanujan, its modular identities and explicit evaluations ⋮ Ramanujan's function \(k\), revisited ⋮ A new proof of Ramanujan's modular equation relating \(R(q)\) with \(R(q^{5})\) ⋮ New general theorems and explicit values of the level 13 analogue of Rogers-Ramanujan continued fraction ⋮ 5-dissections and sign patterns of Ramanujan's parameter and its companion

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