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General Formalism Solving Linear Recursion Relations

Adel F. Antippa and Alain J. Phares
Journal of Mathematical Physics
vol. 18, no. 1, pp. 173-181 (1977)

We give the general solution of multiterm linear homogeneous recursion relations with nonconstant coefficients, by introducing a new class of special combinatorics functions based on the partition of an interval into classes. This provides power series solutions, whenever they exist, of ordinary linear differential equations, of any order, with polynomial coefficients.

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