Polynomial solutions of differential-difference equations

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dc.creatorDominici, Diego
dc.creatorDriver, Kathy
dc.creatorJordaan, Kerstin
dc.date2009-01-31
dc.date.accessioned2026-07-07T12:36:49Z
dc.date.available2026-07-07T12:36:49Z
dc.descriptionWe investigate the zeros of polynomial solutions to the differential-difference equation \[ P_{n+1}(x)=A_{n}(x)P_{n}^{\prime}(x)+B_{n}(x)P_{n}(x), n=0,1,... \] where $A_{n}$ and $B_{n}$ are polynomials of degree at most 2 and 1 respectively. We address the question of when the zeros are real and simple and whether the zeros of polynomials of adjacent degree are interlacing. Our result holds for general classes of polynomials but includes sequences of classical orthogonal polynomials as well as Euler-Frobenius, Bell and other polynomials.
dc.identifierhttps://arxiv.org/abs/0902.0041
dc.identifierhttp://arxiv.org/abs/0902.0041
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/218223
dc.subjectClassical Analysis and ODEs
dc.subject33C45, 42C05
dc.titlePolynomial solutions of differential-difference equations
dc.typetext

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