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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Discrete Painlev equations for recurrence coeffici
ents of orthogonal polynomials - van Assche\, W (K
atholieke Universiteit Leuven)
DTSTART;TZID=Europe/London:20090703T100000
DTEND;TZID=Europe/London:20090703T110000
UID:TALK18961AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/18961
DESCRIPTION:All classical orthogonal polynomials in the Askey
table (and its q-extension) are orthogonal with re
spect to a weight w that satisfies a first order d
ifferential\, (divided) difference or q-difference
equation with polynomial coefficients of degree o
ne and less than or equal to two respectively (Pea
rson equation). Their recurrence coefficients coef
ficients can be found using this Pearson equation
by solving a first order difference equation. Semi
-classical weights satisfy a Pearson equation with
polynomial coefficients of higher degree. The rec
urrence coefficients then satisfy higher order dif
ference equations. Many examples have been worked
out and we will present some of the semi-classical
weights that give rise to discrete Painlev equati
ons for the recurrence coefficients of the orthogo
nal polynomials. This is joint work with my studen
t Lies Boelen.\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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