A q-linear analogue of the plane wave expansion

We obtain a q-linear analogue of Gegenbauerʼs expansion of the plane wave. It is expanded in terms of the little q-Gegenbauer polynomials and the third Jackson q-Bessel function. The result is obtained by using a method based on bilinear biorthogonal expansions.

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Bibliographic Details
Published inAdvances in applied mathematics Vol. 50; no. 3; pp. 415 - 428
Main Authors Abreu, Luís Daniel, Ciaurri, Óscar, Varona, Juan Luis
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.03.2013
Subjects
Analogue
Bilinear expansion
Biorthogonal expansion
Dunkl transform
Fourier–Neumann expansion
Mathematical analysis
Plane wave expansion
Plane waves
q-Special functions
Sampling theorem
Special functions
secondary
Dunkl transform
q-Special functions
Fourier–Neumann expansion
Plane wave expansion
Biorthogonal expansion
Sampling theorem
Special functions
primary
Bilinear expansion
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Summary:We obtain a q-linear analogue of Gegenbauerʼs expansion of the plane wave. It is expanded in terms of the little q-Gegenbauer polynomials and the third Jackson q-Bessel function. The result is obtained by using a method based on bilinear biorthogonal expansions.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0196-8858
1090-2074
DOI:10.1016/j.aam.2012.11.001