Elliptic Integrals and Elliptic Functions

Elliptic Integrals and Elliptic Functions portes grátis

Elliptic Integrals and Elliptic Functions

Takebe, Takashi

Springer International Publishing AG

07/2023

328

Dura

Inglês

9783031302640

15 a 20 dias

Descrição não disponível.

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.

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elliptic functions;elliptic integrals;complex analysis;application to physics;Riemann surfaces;elliptic curves;Abel-Jacobi theorem;addition theorems;theta functions