Expansions in the Askey-Wilson polynomials

Mourad E.H. Ismail; Dennis Stanton

doi:10.1016/j.jmaa.2014.11.048

Expansions in the Askey-Wilson polynomials

Mourad E.H. Ismail, Dennis Stanton

School of Mathematics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

We give a general expansion formula of functions in the Askey-Wilson polynomials and using Askey-Wilson orthogonality we evaluate several integrals. Moreover we give a general expansion formula of functions in polynomials of Askey-Wilson type, which are not necessarily orthogonal. Limiting cases give expansions in little and big q-Jacobi type polynomials. We also give a new generating function for Askey-Wilson polynomials and a new evaluation for specialized Askey-Wilson polynomials.

Original language	English (US)
Pages (from-to)	664-674
Number of pages	11
Journal	Journal of Mathematical Analysis and Applications
Volume	424
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2014.11.048
State	Published - Apr 1 2015

Bibliographical note

Publisher Copyright:
© 2014 Elsevier Inc.

Keywords

Andrews formula
Askey-Wilson polynomials
Basic hypergeometric series
Expansion formulas
Generating functions

Publisher link

10.1016/j.jmaa.2014.11.048

Find It

Find It at U of M Libraries

Cite this

@article{953f5fec67d84a10806a0460d165788c,

title = "Expansions in the Askey-Wilson polynomials",

abstract = "We give a general expansion formula of functions in the Askey-Wilson polynomials and using Askey-Wilson orthogonality we evaluate several integrals. Moreover we give a general expansion formula of functions in polynomials of Askey-Wilson type, which are not necessarily orthogonal. Limiting cases give expansions in little and big q-Jacobi type polynomials. We also give a new generating function for Askey-Wilson polynomials and a new evaluation for specialized Askey-Wilson polynomials.",

keywords = "Andrews formula, Askey-Wilson polynomials, Basic hypergeometric series, Expansion formulas, Generating functions",

author = "Ismail, {Mourad E.H.} and Dennis Stanton",

note = "Publisher Copyright: {\textcopyright} 2014 Elsevier Inc.",

year = "2015",

month = apr,

day = "1",

doi = "10.1016/j.jmaa.2014.11.048",

language = "English (US)",

volume = "424",

pages = "664--674",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - Expansions in the Askey-Wilson polynomials

AU - Ismail, Mourad E.H.

AU - Stanton, Dennis

PY - 2015/4/1

Y1 - 2015/4/1

N2 - We give a general expansion formula of functions in the Askey-Wilson polynomials and using Askey-Wilson orthogonality we evaluate several integrals. Moreover we give a general expansion formula of functions in polynomials of Askey-Wilson type, which are not necessarily orthogonal. Limiting cases give expansions in little and big q-Jacobi type polynomials. We also give a new generating function for Askey-Wilson polynomials and a new evaluation for specialized Askey-Wilson polynomials.

AB - We give a general expansion formula of functions in the Askey-Wilson polynomials and using Askey-Wilson orthogonality we evaluate several integrals. Moreover we give a general expansion formula of functions in polynomials of Askey-Wilson type, which are not necessarily orthogonal. Limiting cases give expansions in little and big q-Jacobi type polynomials. We also give a new generating function for Askey-Wilson polynomials and a new evaluation for specialized Askey-Wilson polynomials.

KW - Andrews formula

KW - Askey-Wilson polynomials

KW - Basic hypergeometric series

KW - Expansion formulas

KW - Generating functions

UR - http://www.scopus.com/inward/record.url?scp=84920605456&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84920605456&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2014.11.048

DO - 10.1016/j.jmaa.2014.11.048

M3 - Article

AN - SCOPUS:84920605456

SN - 0022-247X

VL - 424

SP - 664

EP - 674

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Expansions in the Askey-Wilson polynomials

Abstract

Bibliographical note

Keywords

Publisher link

Find It

Other files and links

Fingerprint

Cite this