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The central two-point connection problem for the Heun class of ODEs. (English) Zbl 0931.34073
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:
34M25Formal solutions, transform techniques (ODE in the complex domain)
83C40Gravitational energy and conservation laws; groups of motions
83C55Macroscopic interaction of the gravitational field with matter (general relativity)
81V17Gravitational interaction