Elliptic Integrals and Elliptic Functions
This book gives a comprehensive introduction to those parts of the theory of elliptic integrals and elliptic functions which provide illuminating examples in complex analysis, but which are not often covered in regular university courses. These examples form prototypes of major ideas in modern mathe...
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| Formato: | Electrónico eBook |
| Idioma: | inglés |
| Publicado: |
Cham :
Springer International Publishing : Imprint: Springer,
2023.
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| Edición: | 1st ed. 2023. |
| Series: | Moscow Lectures,
9 |
| Subjects: | |
| Acceso en liña: | https://doi.org/10.1007/978-3-031-30265-7 |
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Table of Contents:
- Introduction
- Chapter 1. The arc length of curves
- Chapter 2. Classification of elliptic integrals
- Chapter 3. Applications of elliptic integrals
- Chapter 4. Jacobi’s elliptic functions on R
- Chapter 5. Applications of Jacobi’s elliptic functions
- Riemann surfaces of algebraic functions
- Chapter 7. Elliptic curves
- Chapter 8. Complex elliptic integrals
- Chapter 9. Mapping the upper half plane to a rectangle
- Chapter 10. The Abel-Jacobi theorem
- Chapter 11. The general theory of elliptic functions
- Chapter 12. The Weierstrass ℘-function
- Chapter 13. Addition theorems
- Chapter 14. Characterisation by addition formulae
- Chapter 15. Theta functions
- Chapter 16. Infinite product factorisation of theta functions
- Chapter 17. Complex Jacobian functions
- Appendix A. Theorems in analysis and complex analysis
- Bibliography
- Index.