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Perturbation of the coefficients in the recurrence relation of a class of polynomials

✍ Scribed by E.K. Ifantis; P.D. Siafarikas

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
360 KB
Volume
57
Category
Article
ISSN
0377-0427

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Let \(P\_{N+1}(x)\) be the polynomial which is defined recursively by \(P\_{0}(x)=0\), \(P\_{1}(x)=1, \quad\) and \(\alpha\_{n} P\_{n+1}(x)+\alpha\_{n-1} P\_{n-1}(x)+b\_{n} P\_{n}(x)=x d\_{n} P\_{n}(x), \quad n=1, \quad 2, \ldots, N\), where \(\alpha\_{n}, b\_{n}, d\_{n}\) are real sequences with \(

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In this paper we compute the recurrence coefficients of orthogonal polynomials using -function techniques. It is shown that for polynomials orthogonal with respect to positive weight functions on a noncompact interval, the recurrence coefficient can be expressed as the change in the chemical potenti