On Generating Orthogonal Polynomials for Discrete Measures | Zendy

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On Generating Orthogonal Polynomials for Discrete Measures

Author(s) -

Hans-Jürgen Fischer

Publication year - 1998

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/815

Subject(s) - orthogonal polynomials , mathematics , discrete orthogonal polynomials , kravchuk polynomials , classical orthogonal polynomials , algebra over a field , pure mathematics , wilson polynomials

Let oe be a given positive measure with infinite support S(oe) and finite moments of allorders. Then there exists a unique family of monic polynomials ~ ? j withZ~ ? l (x)~? j (x) doe(x) = 0 for l ! j andZ~ ?2j (x) doe(x) = fl\Gamma2j ? 0; j = 0; 1; : : : (1)(fl j is the leading coefficient of the orthonormal polynomial of degree j). They satisfy athree term recurrence relation~ ? j+1 (x) = (x \Gamma ff j )~? j

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