32 Continued Fractions. - 1 The RogersRamanujan Continued Fraction. - 2 Other qContinued Fractions. - 3 Continued Fractions Arising from Products of Gamma Functions. - 4 Other Continued Fractions. - 5 General Theorems. - 33 Ramanujan's Theories of Elliptic Functions to Alternative Bases. - 1 Introduction. - 2 Ramanujan's Cubic Transformation the Borweins' Cubic ThetaFunction Identity and the Inversion Formula. - 3 The Principles of Triplication and Trimidiation. - 4 The Eisenstein Series L M and N. - 5 A Hypergeometric Transformation and Associated Transfer Principle. - 6 More Higher Order Transformations for Hypergeometric Series. - 7 Modular Equations in the Theory of Signature 3. - 8 The Inversion of an Analogue of K (k) in Signature 3. - 9 The Theory for Signature 4. - 10 Modular Equations in the Theory of Signature 4. - 11 The Theory for Signature 6. - 12 An Identity from the First Notebook and Further Hypergeometric Transformations. - 13 Some Enigmatic Formulas Near the End of the Third Notebook. - 14 Concluding Remarks. - 34 Class Invariants and Singular Moduli. - 1 Introduction. - 2 Table of Class Invariants. - 3 Computation of Gnand gnwhen 9/n. - 4 Kronecker's Limit Formula and General Formulas for Class Invariants. - 5 Class Invariants Via Kronecker's Limit Formula. - 6 Class Invariants Via Modular Equations. - 7 Class Invariants Via Class Field Theory. - 8 Miscellaneous Results. - 9 Singular Moduli. - 10 A Certain Rational Function of Singular Moduli. - 11 The Modular j-invariant. - 35 Values of Theta-Functions. - 0 Introduction. - 1 Elementary Values. - 2 Nonelementary Values of. - 3 A Remarkable Product of Theta-Functions. - 36 Modular Equations and Theta-Function Identities in Notebook 1. - 1 Modular Equations of Degree 3 and Related Theta-Function Identities. - 2 Modular Equations of Degree 5 and Related Theta-Function Identities. - 3 Other Modular Equations and Related Theta-Function Identities. - 4 Identities Involving Lambert Series. - 5 Identities Involving Eisenstein Series. - 6 Modular Equations in the Form of Schläfli. - 7 Modular Equations in the Form of Russell. - 8 Modular Equations in the Form of Weber. - 9 Series Transformations Associated with Theta-Functions. - 10 Miscellaneous Results. - 37 Infinite Series. - 38 Approximations and Asymptotic Expansions. - 39 Miscellaneous Results in the First Notebook. - Location of Entries in the Unorganized Portions of Ramanujan's First Notebook. - References. Language: English