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Asymptotic expansions of recursion coefficients of orthogonal polynomials with truncated exponential weights

  • Haewon Joung (a1)
Abstract

Let β > 0 and , define and where a2n denotes Mhaskar-Rahmanov-Staff number for Wβ. Let be the leading coefficients of the nth orthonormal polynomial corresponding to Wβ,cn and write . It is shown that if c > 1 and β is a positive even integer then has an asymptotic expansion. Also when 0 < c < 1, asymptotic expansions of recursion coefficients of the truncated Hermite weights are given.

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Copyright
COPYRIGHT: © Editorial Board of Nagoya Mathematical Journal 2002
References
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[1] Chen, Y. and Ismail, M.E.H., Ladder operators and differential equations for orthogonal polynomials, J. Phys. A, 30, 7817–7829.
[2] Ismail, M.E.H., Discriminants and functions of the second kind of orthogonal polynomials, Result. Math., 34, 132–149.
[3] Lubinsky, D. S. and Saff, E. B., Uniform and mean approximation by certain weighted polynomials, with applications, Constr. Approx., 4 (1988), 21–64.
[4] Mhaskar, H. N. and Saff, E. B., Extremal problems for polynomials with exponential weights, Trans. Amer. Math. Soc., 285 (1984), 203–234.
[5] Máté, A. and Nevai, P., Asymptotics for solutions of smooth recurrence equations, Proc. Amer. Math. Soc., 93 (1985), 423–429.
[6] Máté, A., Nevai, P. and Zaslavsky, T., Asymptotic expansions of ratios of coefficients of orthogonal polynomials with exponential weights, Trans. Amer. Math. Soc., 287 (1985), 495–505.
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Nagoya Mathematical Journal
  • ISSN: 0027-7630
  • EISSN: 2152-6842
  • URL: /core/journals/nagoya-mathematical-journal
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