Local asymptotics of the ratio of orthogonal polynomials in the neighbourhood of an end-point of the support of the orthogonality measure (Q2759320)
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scientific article; zbMATH DE number 1681726
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Local asymptotics of the ratio of orthogonal polynomials in the neighbourhood of an end-point of the support of the orthogonality measure |
scientific article; zbMATH DE number 1681726 |
Statements
Local asymptotics of the ratio of orthogonal polynomials in the neighbourhood of an end-point of the support of the orthogonality measure (English)
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3 January 2002
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ratio asymptotics
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recurrence coefficients
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Riccati's equation
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Bessel functions
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Bernstein-Markov inequality
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orthogonal polynomials
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The author suggests a new method of studying the asymptotic behavior of the ratio of orthogonal polynomials in the neighbourhood of an end-point of the support of the orthogonality measure provided that the corresponding asymptotic behavior at the end-point itself as well as the asymptotics for the coefficients of the three-term recurrence relation is known. As a consequence of the main result the asymptotics of zeros of orthogonal polynomials in question is obtained. The precise constants in the Bernstein-Markov inequalities is discussed.
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