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Book Synopsis
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 P-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.

Elliptic Integrals and Elliptic Functions

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    A Paperback by Takashi Takebe

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      View other formats and editions of Elliptic Integrals and Elliptic Functions by Takashi Takebe

      Publisher: Springer
      Publication Date: 12/07/2024
      ISBN13: 9783031302671, 978-3031302671
      ISBN10:
      Also in:
      Functional analysis and transforms

      Description

      Book Synopsis
      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 P-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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