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Abstract
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We show how to
derive structure relations for general orthogonal polynomials, that is, we
find operators whose action on pn is a combination of pn and pn+1 with
variable coefficients. We also provide an analogue of the string equation
for general orthogonal polynomials. We explore the connection with the
Toda lattice and polynomials orthogonal with respect to general exponential
weights.
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Keywords
general orthogonal polynomials, Freud
weights, Askey–Wilson type polynomials,
Jacobi–Toda weights
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Mathematical Subject Classification
Primary: 42C05
Secondary: 33C45
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Milestones
Received: 11 May 2008
Revised: 12 December 2008
Published: 4 March 2009
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