Moments of askey-wilson polynomials

Jang Soo Kim; Dennis W Stanton

Moments of askey-wilson polynomials

Jang Soo Kim, Dennis W Stanton

Mathematics

Research output: Contribution to journal › Conference article › peer-review

1 Scopus citations

Abstract

New formulas for the n^th moment μ_n(a, b, c, d; q) of the Askey-Wilson polynomials are given. These are derived using analytic techniques, and by considering three combinatorial models for the moments: Motzkin paths, matchings, and staircase tableaux. A related positivity theorem is given and another one is conjectured.

Original language	English (US)
Pages (from-to)	169-180
Number of pages	12
Journal	Discrete Mathematics and Theoretical Computer Science
State	Published - Nov 18 2013
Event	25th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2013 - Paris, France Duration: Jun 24 2013 → Jun 28 2013

Keywords

Askey-wilson polynomials
Hypergeometric series
Moments of orthogonal polynomials
Motzkin paths

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title = "Moments of askey-wilson polynomials",

abstract = "New formulas for the nth moment μn(a, b, c, d; q) of the Askey-Wilson polynomials are given. These are derived using analytic techniques, and by considering three combinatorial models for the moments: Motzkin paths, matchings, and staircase tableaux. A related positivity theorem is given and another one is conjectured.",

keywords = "Askey-wilson polynomials, Hypergeometric series, Moments of orthogonal polynomials, Motzkin paths",

author = "Kim, {Jang Soo} and Stanton, {Dennis W}",

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day = "18",

language = "English (US)",

pages = "169--180",

journal = "Discrete Mathematics and Theoretical Computer Science",

issn = "1462-7264",

publisher = "Maison de l'informatique et des mathematiques discretes",

note = "25th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2013 ; Conference date: 24-06-2013 Through 28-06-2013",

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AU - Kim, Jang Soo

AU - Stanton, Dennis W

PY - 2013/11/18

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N2 - New formulas for the nth moment μn(a, b, c, d; q) of the Askey-Wilson polynomials are given. These are derived using analytic techniques, and by considering three combinatorial models for the moments: Motzkin paths, matchings, and staircase tableaux. A related positivity theorem is given and another one is conjectured.

AB - New formulas for the nth moment μn(a, b, c, d; q) of the Askey-Wilson polynomials are given. These are derived using analytic techniques, and by considering three combinatorial models for the moments: Motzkin paths, matchings, and staircase tableaux. A related positivity theorem is given and another one is conjectured.

KW - Askey-wilson polynomials

KW - Hypergeometric series

KW - Moments of orthogonal polynomials

KW - Motzkin paths

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JO - Discrete Mathematics and Theoretical Computer Science

JF - Discrete Mathematics and Theoretical Computer Science

SN - 1462-7264

T2 - 25th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2013

Y2 - 24 June 2013 through 28 June 2013

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