Royal Society Publishing

Heun's equation with nearby singularities

Wolfgang Lay , Sergei Yu. Slavyanov


The boundary problem for the Heun equation is studied in the case when two singularities of the equation merge. The eigenfunctions are characterized by a sharp peak in a small boundary layer around the merging points. The eigenvalues as functions of the distance between the merging points reveal a non–analytic behaviour in the vicinity of zero.

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