LEADER 04091nam 22005895 450 001 9910734846003321 005 20251202142031.0 010 $a3-031-30265-6 024 7 $a10.1007/978-3-031-30265-7 035 $a(CKB)27559747400041 035 $a(MiAaPQ)EBC30625745 035 $a(Au-PeEL)EBL30625745 035 $a(DE-He213)978-3-031-30265-7 035 $a(PPN)272253944 035 $a(EXLCZ)9927559747400041 100 $a20230710d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aElliptic Integrals and Elliptic Functions /$fby Takashi Takebe 205 $a1st ed. 2023. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2023. 215 $a1 online resource (329 pages) 225 1 $aMoscow Lectures,$x2522-0322 ;$v9 311 08$a9783031302640 320 $aIncludes bibliographical references and index. 327 $aIntroduction -- 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. 330 $aThis book gives a comprehensive introduction to those parts of the theory of elliptic integrals and elliptic functions which provide illuminating examples in complex analysis, but which are not often covered in regular university courses. These examples form prototypes of major ideas in modern mathematics and were a driving force of the subject in the eighteenth and nineteenth centuries. In addition to giving an account of the main topics of the theory, the book also describes many applications, both in mathematics and in physics. For the reader?s convenience, all necessary preliminaries on basic notions such as Riemann surfaces are explained to a level sufficient to read the book. For each notion a clear motivation is given for its study, answering the question ?Why do we consider such objects??, and the theory is developed in a natural way that mirrors its historical development (e.g., ?If there is such and such an object, then you would surely expect this one?). This feature sets this text apart from other books on the same theme, which are usually presented in a different order. Throughout, the concepts are augmented and clarified by numerous illustrations. Suitable for undergraduate and graduate students of mathematics, the book will also be of interest to researchers who are not familiar with elliptic functions and integrals, as well as math enthusiasts. . 410 0$aMoscow Lectures,$x2522-0322 ;$v9 606 $aFunctions, Special 606 $aFunctions of complex variables 606 $aMathematical physics 606 $aSpecial Functions 606 $aFunctions of a Complex Variable 606 $aMathematical Methods in Physics 615 0$aFunctions, Special. 615 0$aFunctions of complex variables. 615 0$aMathematical physics. 615 14$aSpecial Functions. 615 24$aFunctions of a Complex Variable. 615 24$aMathematical Methods in Physics. 676 $a515.983 700 $aTakebe$b Takashi$01373837 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910734846003321 996 $aElliptic Integrals and Elliptic Functions$93404944 997 $aUNINA