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Symbolic solution of nonhomogeneous linear ordinary differential equations in terms of power series

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Abstract

For a nonhomogeneous linear ordinary differential equation Ly(x) = f(x) with polynomial coefficients and a holonomic right-hand side, a set of points x = a is found where a power series solution \(y(x) = \sum\nolimits_{n = 0}^\infty {c_n (x - a)} ^n \) with hypergeometric coefficients exists (starting from some number, the ratio c n + 1/c n is a rational function of n).

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References

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Original Russian Text © A.A. Ryabenko, 2006, published in Programmirovanie, 2006, Vol. 32, No. 2.

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Ryabenko, A.A. Symbolic solution of nonhomogeneous linear ordinary differential equations in terms of power series. Program Comput Soft 32, 120–122 (2006). https://doi.org/10.1134/S0361768806020113

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  • DOI: https://doi.org/10.1134/S0361768806020113

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