• Title/Summary/Keyword: Semi-classical orthogonal polynomials

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COMPATIBLE PAIRS OF ORTHOGONAL POLYNOMIALS

  • Kim, D.H.;Kwon, Kil-H.;Lee, D.W.;Marcellan, F.
    • Bulletin of the Korean Mathematical Society
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    • v.36 no.4
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    • pp.779-797
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    • 1999
  • We find necessary and sufficient conditions for an orthogonal polynomial system to be compatible with another orthogonal polynomial system. As applications, we find new characterizations of semi-classical and clasical orthorgonal polynomials.

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GAUSSIAN QUADRATURE FORMULAS AND LAGUERRE-PERRON@S EQUATION

  • HAJJI S. EL;TOUIJRAT L.
    • Journal of applied mathematics & informatics
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    • v.18 no.1_2
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    • pp.205-228
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    • 2005
  • Let I(f) be the integral defined by : $I(f) = \int\limits_{a}^{b} f(x)w(x)dx$ with f a given function, w a nonclassical weight function and [a, b] an interval of IR (of finite or infinite length). We propose to calculate the approximate value of I(f) by using a new scheme for deriving a non-linear system, satisfied by the three-term recurrence coefficients of semi-classical orthogonal polynomials. Finally we studies the Stability and complexity of this scheme.