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