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SUMMARY:Alta Jooste (University of Pretoria)
DTSTART:20240514T130000Z
DTEND:20240514T140000Z
DTSTAMP:20260422T201825Z
UID:CAvid/120
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/120/">
 Recurrence equations involving orthogonal polynomials with related weight 
 functions</a>\nby Alta Jooste (University of Pretoria) as part of CAvid: C
 omplex Analysis video seminar\n\nLecture held in N/A.\n\nAbstract\nEvery s
 equence of real polynomials $\\{p_n\\}_{n=0}^\\infty=0$\, orthogonal with 
 respect to a positive weight function w(x) on the interval $(a\,b)$\, sati
 sfies a three-term recurrence equation. We discuss the role played by the 
 polynomials associated to $p_n$\, especially as coefficient polynomials in
  the three-term recurrence equation involving polynomials $p_n$\, $p_{n-1}
 $ and $p_{n-m}$\, $m\\in\\{2\,3\,...\,n-1\\}$.  Furthermore\, we show how 
 Christoffel's formula is used to obtain mixed three-term recurrence equati
 ons involving the polynomials $p_n$\, $p_{n-1}$ and\n$g_{n-m\,k}$\, $m \\i
 n \\{2\,3\,...\,n-1\\}$\,\nwhere the sequence $\\{g_{n\,k}\\}_{n=0}^\\inft
 y$\, $k \\in {\\mathbb{N}}_0$\, is orthogonal with respect to $c_k(x)w(x) 
 > 0$ on (a\,b) and $c_k$ is a polynomial of degree $k$ in $x$. We discuss 
 the conditions on $k$\, necessary and sufficient for these equations to be
  in such a form\, that they can be applied in the study of the location of
  the zeros of the appropriate polynomials.\n
LOCATION:https://researchseminars.org/talk/CAvid/120/
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