Plancherel-Rotach Asymptotics for q-Orthogonal Polynomials

Mourad E. H. Ismail; Xin Li

doi:10.1007/s00365-013-9182-6

Plancherel-Rotach Asymptotics for q-Orthogonal Polynomials

Mourad E. H. Ismail
, Xin Li

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

4 Citations (Scopus)

Abstract

We establish the Plancherel-Rotach-type asymptotics around the largest zero (the soft edge asymptotics) for some classes of polynomials satisfying three-term recurrence relations with exponentially increasing coefficients. As special cases, our results include this type of asymptotics for q ^-1-Hermite polynomials of Askey, Ismail, and Masson; q-Laguerre polynomials; and the Stieltjes-Wigert polynomials. We also introduce a one-parameter family of solutions to the q-difference equation of the Ramanujan function. © 2013 Springer Science+Business Media New York.

Original language	English
Pages (from-to)	341-356
Journal	Constructive Approximation
Volume	37
Issue number	3
DOIs	https://doi.org/10.1007/s00365-013-9182-6
Publication status	Published - Jun 2013
Externally published	Yes

Bibliographical note

Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

Funding

The research of Mourad E.H. Ismail is supported by the Research Grants Council of Hong Kong under contract # 101411 and the NPST Program of King Saud University, project number 10-MAT1293-02.

Research Keywords

Asymptotics
Error terms
q-Orthogonal polynomials
Ramanujan function
Recurrence relations

RGC Funding Information

RGC-funded

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10.1007/s00365-013-9182-6

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Cite this

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title = "Plancherel-Rotach Asymptotics for q-Orthogonal Polynomials",

abstract = "We establish the Plancherel-Rotach-type asymptotics around the largest zero (the soft edge asymptotics) for some classes of polynomials satisfying three-term recurrence relations with exponentially increasing coefficients. As special cases, our results include this type of asymptotics for q -1-Hermite polynomials of Askey, Ismail, and Masson; q-Laguerre polynomials; and the Stieltjes-Wigert polynomials. We also introduce a one-parameter family of solutions to the q-difference equation of the Ramanujan function. {\textcopyright} 2013 Springer Science+Business Media New York.",

keywords = "Asymptotics, Error terms, q-Orthogonal polynomials, Ramanujan function, Recurrence relations",

author = "Ismail, \{Mourad E. H.\} and Xin Li",

note = "Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].",

year = "2013",

month = jun,

doi = "10.1007/s00365-013-9182-6",

language = "English",

volume = "37",

pages = "341--356",

journal = "Constructive Approximation",

issn = "0176-4276",

publisher = "Springer New York",

number = "3",

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TY - JOUR

T1 - Plancherel-Rotach Asymptotics for q-Orthogonal Polynomials

AU - Ismail, Mourad E. H.

AU - Li, Xin

N1 - Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

PY - 2013/6

Y1 - 2013/6

N2 - We establish the Plancherel-Rotach-type asymptotics around the largest zero (the soft edge asymptotics) for some classes of polynomials satisfying three-term recurrence relations with exponentially increasing coefficients. As special cases, our results include this type of asymptotics for q -1-Hermite polynomials of Askey, Ismail, and Masson; q-Laguerre polynomials; and the Stieltjes-Wigert polynomials. We also introduce a one-parameter family of solutions to the q-difference equation of the Ramanujan function. © 2013 Springer Science+Business Media New York.

AB - We establish the Plancherel-Rotach-type asymptotics around the largest zero (the soft edge asymptotics) for some classes of polynomials satisfying three-term recurrence relations with exponentially increasing coefficients. As special cases, our results include this type of asymptotics for q -1-Hermite polynomials of Askey, Ismail, and Masson; q-Laguerre polynomials; and the Stieltjes-Wigert polynomials. We also introduce a one-parameter family of solutions to the q-difference equation of the Ramanujan function. © 2013 Springer Science+Business Media New York.

KW - Asymptotics

KW - Error terms

KW - q-Orthogonal polynomials

KW - Ramanujan function

KW - Recurrence relations

UR - https://www.scopus.com/pages/publications/84877799329

UR - https://www.scopus.com/pages/publications/84877799329#tab=impact

U2 - 10.1007/s00365-013-9182-6

DO - 10.1007/s00365-013-9182-6

M3 - RGC 21 - Publication in refereed journal

SN - 0176-4276

VL - 37

SP - 341

EP - 356

JO - Constructive Approximation

JF - Constructive Approximation

IS - 3

ER -

Plancherel-Rotach Asymptotics for q-Orthogonal Polynomials

Abstract

Bibliographical note

Funding

Research Keywords

RGC Funding Information

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GRF: Orthogonal Polynomials and q-Series

Cite this

Plancherel-Rotach Asymptotics for q-Orthogonal Polynomials

Abstract

Bibliographical note

Funding

Research Keywords

RGC Funding Information

Access Output

Other Access Options

Permanent Link

Other Files and Links

Fingerprint

Projects

GRF: Orthogonal Polynomials and q-Series

Cite this