Note on two modular equations of Ramanujan
Publication details: New Delhi Springer 2024Edition: Vol.55(1), MarDescription: 47-53pSubject(s): Online resources: In: Indian journal of pure and applied mathematicsSummary: In his notebooks and lost notebook, Ramanujan recorded two modular equations involving the Rogers–Ramanujan continued fraction. These two modular equations were subsequently proved by several scholars. In this paper, we provide another proof for these two modular equations in terms of the 5-dissections of the Euler product , its reciprocal, and Ramanujan’s theta function . As by-products, we also establish four q-series identities concerning some specialized Jacobi theta series.| Item type | Current library | Status | Barcode | |
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School of Engineering & Technology Archieval Section | Not for loan | 2024-1548 |
In his notebooks and lost notebook, Ramanujan recorded two modular equations involving the Rogers–Ramanujan continued fraction. These two modular equations were subsequently proved by several scholars. In this paper, we provide another proof for these two modular equations in terms of the 5-dissections of the Euler product , its reciprocal, and Ramanujan’s theta function . As by-products, we also establish four q-series identities concerning some specialized Jacobi theta series.
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