×
Álvarez-Nodarse, R.; Arvesú, J.

On the \(q\)-polynomials in the exponential lattice \(x(s)=c_1q^s+c_3\). (English) Zbl 0956.33009

Integral Transforms Spec. Funct. 8, No. 3-4, 299-324 (1999).
The authors study \(q\)-analogues in the non-uniform exponential lattice \(x(s)=c_1q^s+c_3\) of the discrete orthogonal polynomials. In the first part of this survey paper the authors describe general properties of the \(q\)-polynomials on non-uniform lattices. In the second part special emphasis is given to the case of the exponential lattice. Then the special case of \(q\)-analogues of the Hahn, Meixner and Krawtchouk polynomials is described. And in the last part the special case of \(q\)-analogues of the Charlier polynomials is treated in more details.
Reviewer: Roelof Koekoek (Delft)

Cited in 15 Documents

MSC:

33D45 Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)

Keywords:

discrete \(q\)-orthogonal polynomials; \(q\)-Charlier polynomials
Cite Review PDF
Full Text: DOI

References:

[1] Álvarez-Nodarse R., Monografi as de la Academia de Ciencias de Zaragoza (1999)
[2] DOI: 10.1088/0305-4470/30/19/015 · Zbl 0930.33010 · doi:10.1088/0305-4470/30/19/015
[3] DOI: 10.1088/0305-4470/29/22/016 · Zbl 0932.33026 · doi:10.1088/0305-4470/29/22/016
[4] DOI: 10.1088/0305-4470/29/7/015 · Zbl 0912.33011 · doi:10.1088/0305-4470/29/7/015
[5] Andrews G.E., Conference Series in Mathematics (1986)
[6] DOI: 10.1016/S0377-0427(98)00002-8 · Zbl 0934.33014 · doi:10.1016/S0377-0427(98)00002-8
[7] Arvesú J., Propiedades analiticas y algebraicas de polinomios con diversos modelos de ortogonalidad: q-Discretos, Tipo Sobolev y Semiclásicos (1999)
[8] Askey R., Symmetries in Science pp 57– (1993)
[9] DOI: 10.1088/0305-4470/26/15/014 · Zbl 0859.33021 · doi:10.1088/0305-4470/26/15/014
[10] DOI: 10.1007/BF00749728 · Zbl 0919.33010 · doi:10.1007/BF00749728
[11] DOI: 10.1137/0510092 · Zbl 0437.33014 · doi:10.1137/0510092
[12] DOI: 10.1007/BF01203415 · Zbl 0837.33010 · doi:10.1007/BF01203415
[13] Atakishiyev N.M., Rev. Mexicana Fis 34 pp 152– (1988)
[14] Atakishiyev N.M., Rev. Mexicana Fis. 34 pp 152– (1988)
[15] DOI: 10.1007/BF01016585 · Zbl 1189.81100 · doi:10.1007/BF01016585
[16] Atakishiyev N.M., Theoretical and Mathematical Phyxics 87 pp 1055– (1991)
[17] DOI: 10.1007/BF01279025 · Zbl 0762.33004 · doi:10.1007/BF01279025
[18] DOI: 10.1088/0305-4470/22/18/004 · Zbl 0708.17015 · doi:10.1088/0305-4470/22/18/004
[19] DOI: 10.1016/0377-0427(93)E0236-F · Zbl 0824.33011 · doi:10.1016/0377-0427(93)E0236-F
[20] Chihara T.S., An Introdution to Orthogonal Polynomials (1978) · Zbl 0389.33008
[21] DOI: 10.1016/0771-050X(79)90025-1 · Zbl 0436.33010 · doi:10.1016/0771-050X(79)90025-1
[22] DOI: 10.1080/10652469608819120 · Zbl 0867.33014 · doi:10.1080/10652469608819120
[23] DOI: 10.1063/1.530728 · Zbl 0829.17008 · doi:10.1063/1.530728
[24] Fine N.J., Mathematical Surveys and Monographs 27 (1988)
[25] Gasper G., Basic Hypergeometric Series (1990) · Zbl 0695.33001
[26] Koekoek R., Reports of the Faculty of Technical Mathematics and Informatics pp 98– (1998)
[27] Koornwinder T.H., In Orthogonal Polynomials. Theory and Practice 294 pp 257– (1990) · Zbl 0697.42019 · doi:10.1007/978-94-009-0501-6_12
[28] Koornwinder T.H., Pitman Research Notes in Mathematics series 311 pp 46– (1994)
[29] DOI: 10.1016/S0377-0427(98)00162-9 · Zbl 0933.33012 · doi:10.1016/S0377-0427(98)00162-9
[30] DOI: 10.1088/0305-4470/22/21/020 · Zbl 0722.17009 · doi:10.1088/0305-4470/22/21/020
[31] Malashin A.A., In Quantum Symmetries pp 223– (1993)
[32] DOI: 10.1007/BF00998681 · Zbl 0793.33009 · doi:10.1007/BF00998681
[33] Medem J.C., Tesis Doctoral (1996)
[34] Nikiforov A.F., Springer Series in Computational Physics (1991)
[35] Nikiforov A.F., Preprint Inst. Prikl. Mat. Im. M.V. Keldysha Akad. Nauk SSSR. 17 (1983)
[36] Nikiforov A.F., Special Functions of Mathematical Physics 17 (1988) · Zbl 0624.33001 · doi:10.1007/978-1-4757-1595-8
[37] Nikiforov A.F., In Proceedings of the Workshop on Symmetries and Integrability of Difference Equations 7 pp 321– (1996)
[38] Smirnov YU.F., In International Workshop Symmetry Methods in Physics in Memory of Professor 2 pp 479– (1994)
[39] Suslov S.K., Uspekhi Mat. Nauk 44 pp 185– (1989)
[40] DOI: 10.1070/RM1989v044n02ABEH002045 · Zbl 0685.33013 · doi:10.1070/RM1989v044n02ABEH002045
[41] Vilenkin N.Ja., Representation of Lie Groups and Special Functions (1992) · doi:10.1007/978-94-017-2881-2
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.