Author | Berndt, Bruce C. author |
---|---|
Title | Ramanujan's Notebooks [electronic resource] : Part V / by Bruce C. Berndt |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1998 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-1624-7 |
Descript | XIII, 624 p. online resource |
32 Continued Fractions -- 1 The RogersโRamanujan Continued Fraction -- 2 Other qโContinued 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 ThetaโFunction 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 Schlรคfli -- 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