Abstract
Ramanujan recorded several hundred modular equations in his three notebooks [7]; no other mathematician has ever discovered nearly so many. Complete proofs for all the modular equations in Ramanujan’s three notebooks can be found in Berndt’s books [1]—[3]. In particular, Chapters 19—21 in Ramanujan’s second notebook are almost exclusively devoted to modular equations. Ramanujan used modular equations to evaluate class invariants, certain q-continued fractions including the Rogers-Ramanujan continued fraction, theta-functions, and certain other quotients and products of theta-functions and eta-functions [3].
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References
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© 2000 Hindustan Book Agency (India) and Indian National Science Academy
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Berndt, B.C. (2000). Modular Equations in Ramanujan’s Lost Notebook. In: Bambah, R.P., Dumir, V.C., Hans-Gill, R.J. (eds) Number Theory. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7023-8_4
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DOI: https://doi.org/10.1007/978-3-0348-7023-8_4
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