Document Zbl 1083.15011

Determinants with orthogonal polynomial entries. (English) Zbl 1083.15011

J. Comput. Appl. Math. 178, No. 1-2, 255-266 (2005).

The author uses moment representations of orthogonal polynomials to evaluate the corresponding Hankel determinants formed by the orthogonal polynomials. He also studies the Hankel determinants which start with the orthogonal polynomial \(p_n\) on the top left-hand corner. As an example, he evaluates the Hankel determinants whose entries are \(q\)-ultraspherical or Al-Salam-Chihara polynomials.

Reviewer: Fuad Kittaneh (Amman)

Cited in 13 Documents

MSC:

15A15	Determinants, permanents, traces, other special matrix functions
42A70	Trigonometric moment problems in one variable harmonic analysis
42C05	Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis

Keywords:

Turan determinants; moments; Hankel determinants; Al-Salam-Chihara polynomials; \(q\)-ultraspherical polynomials

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References:

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