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  1. Home
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  3. Elliptic Functions
  • Cited by 42
Publisher:
Cambridge University Press
Online publication date:
December 2009
Print publication year:
2006
Online ISBN:
9780511617867
DOI:
https://doi.org/10.1017/CBO9780511617867
Subjects:
Mathematics (general), Mathematics, Number Theory
Series:
London Mathematical Society Student Texts (67)
Information

Book description

In its first six chapters this 2006 text seeks to present the basic ideas and properties of the Jacobi elliptic functions as an historical essay, an attempt to answer the fascinating question: 'what would the treatment of elliptic functions have been like if Abel had developed the ideas, rather than Jacobi?' Accordingly, it is based on the idea of inverting integrals which arise in the theory of differential equations and, in particular, the differential equation that describes the motion of a simple pendulum. The later chapters present a more conventional approach to the Weierstrass functions and to elliptic integrals, and then the reader is introduced to the richly varied applications of the elliptic and related functions. Applications spanning arithmetic (solution of the general quintic, the functional equation of the Riemann zeta function), dynamics (orbits, Euler's equations, Green's functions), and also probability and statistics, are discussed.

Reviews

'This solid text is a good place to start when working with elliptic functions and it is the sort of book that you will keep coming back to as reference text.'

Source: Mathematics Today

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Contents

Contents
References
References
Further reading
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