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Original Articles

Structure relations for q-polynomials and some applications

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Pages 747-767 | Received 17 Aug 2009, Accepted 06 Jun 2010, Published online: 17 Dec 2010

References

  • Ismail , MEH . 2005 . Classical and Quantum Orthogonal Polynomials in one Variable , Cambridge : Cambridge University Press .
  • Chen , Y and Ismail , MEH . 2008 . Ladder operators for q-orthogonal polynomials . J. Math. Anal. Appl. , 345 : 1 – 10 .
  • Ismail , MEH and Simeonov , P . 2009 . q-difference operators for orthogonal polynomials . J. Comput. Appl. Math. , 233 ( 3 ) : 749 – 761 .
  • Szegő , G . 1975 . Orthogonal Polynomials, , 4th , Providence : American Mathematical Society .
  • Koekoek , R and Swarttouw , R . 1998 . “ The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogues ” . In Reports of the Faculty of Technical Mathematics and Informatics No. 98-17 , Delft : Delft University of Technology .
  • Ismail , MEH and Mansour , ZS . q-Analogue of Freud weights and nonlinear difference equations . Adv. Appl. Math. , forthcoming, doi:10.1016/j.aam.2010.02.003
  • Ramani , A and Grammaticos , B . 1996 . Discrete Painlevé equations: Coalescences, limits and degeneracies . Physica A , 228 : 160 – 171 .
  • Gasper , G and Rahman , M . 2004 . Basic Hypergeometric Series, , 2nd , Cambridge : Cambridge University Press .
  • Ismail , MEH . 2005 . Asymptotics of q-orthogonal polynomials and a q-Airy function . IMRN , 18 : 1063 – 1088 .

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