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Development of elliptic functions according to Ramanujan [[electronic resource] /] / originally by K. Venkatachaliengar ; edited and revised by Shaun Cooper
| Development of elliptic functions according to Ramanujan [[electronic resource] /] / originally by K. Venkatachaliengar ; edited and revised by Shaun Cooper |
| Autore | Venkatachaliengar K |
| Edizione | [[Rev. ed.].] |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, N.J., : World Scientific, c2012 |
| Descrizione fisica | 1 online resource (185 p.) |
| Disciplina | 515.983 |
| Altri autori (Persone) | CooperShaun |
| Collana | Monographs in number theory |
| Soggetto topico | Elliptic functions |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-280-37754-2
9786613555458 981-4366-46-3 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; 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 1ψ1 summation formula; 2.3 Ramanujan's transcendentals U2n and V2n; 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 2F1(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 2F1(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 2F1(1/4, 3/4; 1; x); 5.5 The hypergeometric function 2F1(1/6, 5/6; 1; x); 5.6 The hypergeometric function 2F1(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 λ; 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; Appendix A Singular Moduli; A.1 Notes; Appendix B The Quintuple Product Identity; B.1 Notes; Appendix C Addition Theorem of Elliptic Integrals; Bibliography; Index |
| Record Nr. | UNINA-9910457165303321 |
Venkatachaliengar K
|
||
| Singapore ; ; Hackensack, N.J., : World Scientific, c2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Development of elliptic functions according to Ramanujan [[electronic resource] /] / originally by K. Venkatachaliengar ; edited and revised by Shaun Cooper
| Development of elliptic functions according to Ramanujan [[electronic resource] /] / originally by K. Venkatachaliengar ; edited and revised by Shaun Cooper |
| Autore | Venkatachaliengar K |
| Edizione | [[Rev. ed.].] |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, N.J., : World Scientific, c2012 |
| Descrizione fisica | 1 online resource (185 p.) |
| Disciplina | 515.983 |
| Altri autori (Persone) | CooperShaun |
| Collana | Monographs in number theory |
| Soggetto topico | Elliptic functions |
| ISBN |
1-280-37754-2
9786613555458 981-4366-46-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; 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 1ψ1 summation formula; 2.3 Ramanujan's transcendentals U2n and V2n; 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 2F1(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 2F1(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 2F1(1/4, 3/4; 1; x); 5.5 The hypergeometric function 2F1(1/6, 5/6; 1; x); 5.6 The hypergeometric function 2F1(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 λ; 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; Appendix A Singular Moduli; A.1 Notes; Appendix B The Quintuple Product Identity; B.1 Notes; Appendix C Addition Theorem of Elliptic Integrals; Bibliography; Index |
| Record Nr. | UNINA-9910778824403321 |
|
Venkatachaliengar K
|
||
| Singapore ; ; Hackensack, N.J., : World Scientific, c2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Development of elliptic functions according to Ramanujan / / originally by K. Venkatachaliengar ; edited and revised by Shaun Cooper
| Development of elliptic functions according to Ramanujan / / originally by K. Venkatachaliengar ; edited and revised by Shaun Cooper |
| Autore | Venkatachaliengar K |
| Edizione | [[Rev. ed.].] |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, N.J., : World Scientific, c2012 |
| Descrizione fisica | 1 online resource (185 p.) |
| Disciplina | 515.983 |
| Altri autori (Persone) | CooperShaun |
| Collana | Monographs in number theory |
| Soggetto topico | Elliptic functions |
| ISBN |
1-280-37754-2
9786613555458 981-4366-46-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; 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 1ψ1 summation formula; 2.3 Ramanujan's transcendentals U2n and V2n; 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 2F1(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 2F1(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 2F1(1/4, 3/4; 1; x); 5.5 The hypergeometric function 2F1(1/6, 5/6; 1; x); 5.6 The hypergeometric function 2F1(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 λ; 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; Appendix A Singular Moduli; A.1 Notes; Appendix B The Quintuple Product Identity; B.1 Notes; Appendix C Addition Theorem of Elliptic Integrals; Bibliography; Index |
| Record Nr. | UNINA-9910821090203321 |
|
Venkatachaliengar K
|
||
| Singapore ; ; Hackensack, N.J., : World Scientific, c2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||