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).
Similar content being viewed by others
References
Abramov, S.A., Bronstein, M., and Petrovšek, M., On Polynomial Solutions of Linear Operator Equations, Proc. of ISSAC’95 (Montreal, 1995), Levelt, T., Ed., New York: ACM, 1995, pp. 290–296.
Abramov, S.A., Petkovšek, M., and Ryabenko, A., Special Formal Series Solutions of Linear Operator Equations, Discrete Math., 2000, vol. 210, pp. 3–25.
Ryabenko, A.A., Maple Package for Symbolic Construction of Solutions of Linear Ordinary Differential Equations in the Form of Power Series, Programmirovanie, 1999, no. 5, pp. 71–80.
Petkovšek, M., Hypergeometric Solutions of Linear Recurrences with Polynomial Coefficients, Symbolic Computation, 1992, vol. 14, pp. 243–264.
Author information
Authors and Affiliations
Additional information
Original Russian Text © A.A. Ryabenko, 2006, published in Programmirovanie, 2006, Vol. 32, No. 2.
Rights and permissions
About this article
Cite this article
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
Received:
Issue Date:
DOI: https://doi.org/10.1134/S0361768806020113