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1 LPTHE - Laboratoire de Physique Théorique et Hautes Energies 2 LUMIMATH - Departement de Mathematiques Marseille

Abstract : 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.

Keywords : Heun functions elliptic functions Picard theorem finite-gap solutions

Author: Galliano Valent -

Source: https://hal.archives-ouvertes.fr/


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