Transcription of Elliptic Integrals, Elliptic Functions and Theta Functions
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Elliptic Integrals, Elliptic Functions and Theta Functions
Elliptic Integrals, Elliptic Functions and Theta Functions Reading Problems Outline Background .. 2. theory .. 6. Elliptic Integral .. 6. Elliptic Function .. 14. Theta Function .. 16. Assigned Problems .. 17. References .. 20. 1. Background This chapter deals with the Legendre Elliptic integrals, the Theta Functions and the Jaco- bian Elliptic Functions . These Elliptic integrals and Functions nd many applications in the theory of numbers, algebra, geometry, linear and non-linear ordinary and partial di erential equations, dynamics, mechanics, electrostatics, conduction and eld theory . An Elliptic integral is any integral of the general form . A(x) + B(x). f (x) = ! dx C(x) + D(x) S(x).
theory of numbers, algebra, geometry, linear and non-linear ordinary and partial differential equations, dynamics, mechanics, electrostatics, conduction and field theory. An elliptic integral is any integral of the general form f(x)= A(x)+B(x) C(x)+D(x)! S(x) dx where A(x),B(x),C(x) and D(x) are polynomials in x and S(x) is a polynomial of ...
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