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Formulas for recurrence coefficients of orthogonal polynomials related to Lorentzian-like weights

✍ Scribed by Alphonse P. Magnus; Viviane Pierrard


Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
211 KB
Volume
219
Category
Article
ISSN
0377-0427

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✦ Synopsis


One considers the recurrence relation of orthogonal polynomials related to weights |t| A (1 + t 2r /c 2r ) -B on the whole real line, for various integer exponents 2r, and real A > -1, B > 0.


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We consider orthogonal polynomials {p n,N (x)} ∞ n=0 on the real line with respect to a weight w(x) = e -NV (x) and in particular the asymptotic behaviour of the coefficients a n,N and b n,N in the three-term recurrence For one-cut regular V we show, using the Deift-Zhou method of steepest descent