Ramanujan recorded several hundred modular equations in his three notebooks ; 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 –. 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 .
|Original language||English (US)|
|Title of host publication||Number Theory|
|Editors||R P Bambah, V C Dumir, R J Hans-Gill|
|Number of pages||20|
|State||Published - 2000|