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SUMMARY:Polynomial solutions of differential-difference equations - Domini
 ci\, D (State University of New York)
DTSTART:20090630T133000Z
DTEND:20090630T140000Z
UID:TALK18981@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We investigate the zeros of polynomial solutions to the differ
 ential-difference equation [ P_{n+1}(x)=A_{n}(x)P_{n}^{prime}(x)+B_{n}(x)P
 _{n}(x)\,~ n=0\,1\,dots ] where $A_n$ and $B_n$ are polynomials of degree 
 at most $2$ and $1$ respectively. We address the question of when the zero
 s are real and simple and whether the zeros of polynomials of adjacent deg
 ree are interlacing. Our result holds for general classes of polynomials b
 ut includes sequences of classical orthogonal polynomials as well as Euler
 -Frobenius\, Bell and other polynomials.\n
LOCATION:Seminar Room 1\, Newton Institute
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