WKB Approximation and Krall-Type Orthogonal Polynomials
نویسنده
چکیده
Abstract. We give a unified approach to the Krall-type polynomials orthogonal with respect to a positive measure consisting of an absolutely continuous one ‘perturbed’ by the addition of one or more Dirac delta functions. Some examples studied by different authors are considered from a unique point of view. Also some properties of the Krall-type polynomials are studied. The threeterm recurrence relation is calculated explicitly, as well as some asymptotic formulas. With special emphasis will be considered the second order differential equations that such polynomials satisfy. They allow us to obtain the central moments and the WKB approximation of the distribution of zeros. Some examples coming from quadratic polynomial mappings and tridiagonal periodic matrices are also studied.
منابع مشابه
On the Krall-type polynomials
Using a general and simple algebraic approach, some results on Krall-type orthogonal polynomials and some of their extensions are obtained. E-mail: [email protected], [email protected], [email protected]
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