Development of elliptic functions according to Ramanujan /

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This unique book provides an innovative and efficient approach to elliptic functions, based on the ideas of the great Indian mathematician Srinivasa Ramanujan. The original 1988 monograph of K Venkatachaliengar has been completely revised. Many details, omitted from the original version, have been i...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Venkatachaliengar, K.
Autor Corporativo: World Scientific (Firm)
Otros Autores: Cooper, Shaun
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Singapore ; Hackensack, N.J. : World Scientific Pub. Co., Ã2012.
Colección:Monographs in number theory ; v. 6.
Temas:
Elliptic functions.
Fonctions elliptiques.
Elliptic functions
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 1. The Basic Identity. 1.1. Introduction. 1.2. The generalized Ramanujan identity. 1.3. The Weierstrass elliptic function. 1.4. Notes
  • 2. The differential equations of P, Q and R. 2.1. Ramanujan's differential equations. 2.2. Ramanujan's [symbol] summation formula. 2.3. Ramanujan's transcendentals U[symbol] and V[symbol]. 2.4. The imaginary transformation and Dedekind's eta-function. 2.5. Notes
  • 3. The Jordan-Kronecker Function. 3.1. The Jordan-Kronecker function. 3.2. The fundamental multiplicative identity. 3.3. Partitions. 3.4. The hypergeometric function [symbol](1/2, 1/2; 1; x): first method. 3.5. Notes
  • 4. The Weierstrassian invariants. 4.1. Halphen's differential equations. 4.2. Jacobi's identities and sums of two and four squares. 4.3. Quadratic transformations. 4.4. The hypergeometric function [symbol](1/2, 1/2; 1; x): second method. 4.5. Notes
  • 5. The Weierstrassian invariants, II. 5.1. Parameterizations of Eisenstein series. 5.2. Sums of eight squares and sums of eight triangular numbers. 5.3. Quadratic transformations. 5.4. The hypergeometric function [symbol](1/4, 3/4; 1; x). 5.5. The hypergeometric function [symbol](1/6, 5/6; 1; x). 5.6. The hypergeometric function [symbol](1/3, 2/3; 1; x). 5.7. Notes
  • 6. Development of elliptic functions. 6.1. Introduction. 6.2. Jacobian elliptic functions. 6.3. Reciprocals and quotients. 6.4. Derivatives. 6.5. Addition formulas. 6.6. Notes
  • 7. The modular function [symbol]. 7.1. Introduction. 7.2. Modular equations. 7.3. Modular equation of degree 3. 7.4. Modular equation of degree 5. 7.5. Modular equation of degree 7. 7.6. Modular equation of degree 11. 7.7. Modular equation of degree 23. 7.8. Notes.

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