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Zbl 0931.34073
Lay, Wolfgang; Slavyanov, Sergei Yu.
The central two-point connection problem for the Heun class of ODEs. (English)
[J] J. Phys. A, Math. Gen. 31, No.18, 4249-4261 (1998). ISSN 0305-4470

Summary: The authors present a numerical approach to the central two-point connection problem for the confluent cases of the Heun class of differential equations. The crucial step is an ansatz for the solutions to the equations in terms of a generalized power series (so-called Jaffé expansions). It is shown that the resulting difference equations for the coefficients of these series are of Poincaré-Perron type. A (formal) asymptotic investigation of the solutions to these difference equations yields an exact eigenvalue condition.

MSC 2000:: *34M25 Formal solutions, transform techniques
83C40 Groups of motions, etc.
83C55 Hydrodynamics (general relativity)
81V17 Gravitational interaction

Keywords: confluent Heun differential equations; central two-point connection problem; generalized power series; Jaffé expansions

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