Heun functions versus elliptic functions

Details Heun functions versus elliptic functions Heun functions versus elliptic functions

2005-12-02

arxiv.org/abs/math-ph/0512006v1

Physics

Mathematical Physics

Communication at the International Conference on Difference Equations, Special Functions and Applications, Munich, 25-30 july

Scientific paper

We present some recent progresses on Heun functions, gathering results from classical analysis up to elliptic functions. We describe Picard's generalization of Floquet's theory for differential equations with doubly periodic coefficients and give the detailed forms of the level one Heun functions in terms of Jacobi theta functions. The finite-gap solutions give an interesting alternative integral representation which, at level one, is shown to be equivalent to their elliptic form.

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