Kuznetsov, V. B. (ed.), The Kowalevski property. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-2885-1/pbk). CRM Proc. Lect. Notes 32, 287-305 (2002).
Summary: We find a new class of algebraic geometric solutions of Heun’s equation with the accessory parameter belonging to a hyperelliptic curve. Dependence of these solutions from the accessory parameter as well as their relation to Heun’s polynomials are studied. Methods for calculating the algebraic genus of the curve, and its branching points, are suggested. Monodromy group is considered. Numerous examples are given.
|34M35||Singularities, monodromy, local behavior of solutions, normal forms|
|33E30||Functions coming from differential, difference and integral equations|
|33E10||Lamé, Mathieu, and spheroidal wave functions|
|34L40||Particular ordinary differential operators|