The Connection Problem for General Linear Ordinary Differential Equations at Two Regular Singular Points with Applications in the Theory of Special Functions

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Abstract
A two point connection problem for local solutions at two regular singularities of a general linear ordinary differential equation is studied. Explicit formulas for the connection coefficients are obtained which have a wide field of applications especially in the theory of special functions of mathematical physics. Applications to the ellipsoidal wave equation and to Heun’s equation are considered.