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Abramov, Sergei A.; van Hoeij, Mark

Integration of solutions of linear functional equations. (English) Zbl 0939.34059

Integral Transforms Spec. Funct. 8, No. 1-2, 3-12 (1999).
Summary: The authors introduce the notion of the adjoint Ore ring and give a definition of an adjoint polynomial, operator and equation. They apply this for integrating solutions of Ore equations.

Cited in 19 Documents

MSC:

34K06 Linear functional-differential equations
34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
33C05 Classical hypergeometric functions, \({}_2F_1\)
34A45 Theoretical approximation of solutions to ordinary differential equations
34K17 Transformation and reduction of functional-differential equations and systems, normal forms

Keywords:

Ore ring; adjoint; integrating factor; integration; summation; special function; hypergeometric sequence
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References:

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[11] van Hoeij M., Proc. ISSAC’96 pp 219– (1996) · doi:10.1145/236869.237078
[12] Ore O., Ann. Maths 34 pp 480– (1933) · Zbl 0007.15101 · doi:10.2307/1968173
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