כניסה עם גוגל
כניסה עם פייסבוק
Collected papers / Edited by G. H. Hardy, P. V. Seshu Aiyar and B. M. Wilson.
Srinivasa Ramanujan Aiyangar 1887-1920
ספרבחרו את שפת העמוד:
שפה נוכחית
Development of elliptic functions according to Ramanujan [electronic resource]
להגדלת הטקסט להקטנת הטקסט- ספר
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 included, and the book has been made comprehensive by notes at the end of each chapter. The book is for graduate students and researchers in Number Theory and Classical Analysis, as well for scholars and aficionados of Ramanujan's work. It can be read by anyone with some undergraduate knowledge of
| כותר |
Development of elliptic functions according to Ramanujan [electronic resource] / originally by K. Venkatachaliengar edited and revised by Shaun Cooper. |
|---|---|
| מהדורה |
[Rev. ed.]. |
| מוציא לאור |
Singapore Hackensack, N.J. : World Scientific |
| שנה |
c2012 |
| הערות |
Originally published as a Technical Report 2 by Madurai Kamaraj University in February, 1988. Includes bibliographical references and index. English |
| הערת תוכן ותקציר |
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 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 x) 5.5 The hypergeometric function 2F1(1/6, 5/6 5.6 The hypergeometric function 2F1(1/3, 2/3 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 |
| סדרה |
Monographs in number theory, 1793-8341 v. 6 |
| היקף החומר |
1 online resource (185 p.) |
| שפה |
אנגלית |
| מספר מערכת |
997010707439905171 |
תצוגת MARC
תגיות
- Ramanujan Aiyangar, Srinivasa, 1887-1920.
- Ṣrīnivāsa-Rāmānuja Aiyaṅgār, 1887-1920
- Ramanujan, Srinivasa, 1887-1920
- Aiyangar, Srinivasa Ramanujan, 1887-1920
- Iyengar, Srinivasa Iyengar Ramanuja, 1887-1920
- Ramanuja Iyengar, Srinivasa Iyengar, 1887-1920
- Ramanudzhan Aĭengar, 1887-1920
- Ramanujan, S. (Srinivasa), 1887-1920
- Ramanujam, S. (Srinivasa), 1887-1920
- Elliptic functions.
- Elliptic integrals
- nne Functions, Elliptic
- Integrals, Elliptic
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