| Title:
|
A study of $q$-Laguerre polynomials through the $T_{k,q,x}$-operator (English) |
| Author:
|
Khan, M. A. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
47 |
| Issue:
|
4 |
| Year:
|
1997 |
| Pages:
|
619-626 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The present paper deals with certain generating functions and recurrence relations for $q$-Laguerre polynomials through the use of the $T_{k,q,x}$-operator introduced in an earlier paper [7]. (English) |
| MSC:
|
26A33 |
| MSC:
|
33C45 |
| MSC:
|
33D45 |
| idZBL:
|
Zbl 0899.33007 |
| idMR:
|
MR1479308 |
| . |
| Date available:
|
2009-09-24T10:08:55Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127382 |
| . |
| Reference:
|
[1] W. A. Al-salam: Operational representation for the Laguerre and Hermite polynomials.Duke Math. Journal 31 (1964), 127–142. MR 0159053 |
| Reference:
|
[2] W. A. Al-salam, L. Carlitz: Some orthogonal $q$-polynomials.Math. Nachr. 30 (1965), 47–61. MR 0197804, 10.1002/mana.19650300105 |
| Reference:
|
[3] W. Hahn: Beitrage zur Theorie der Heineschen Reihen, Die 24 Integrale der hypergeometrischen $q$-Differenzengleichung, Das $q$-Analogen der Laplace Transformation.Math. Nachr. 2 (1949), 340–379. MR 0035344, 10.1002/mana.19490020604 |
| Reference:
|
[4] M. A. Khan: Certain fractional $q$-integrals and $q$-derivatives.Nanta Mathematica 7 (1974), no. 1, 52–60. Zbl 0289.33009, MR 0369630 |
| Reference:
|
[5] M. A. Khan: On $q$-Laguerre polynomials.Ganita 34 (1983), no. 1 and 2, 111–123. Zbl 0638.33006, MR 0910619 |
| Reference:
|
[6] M. A. Khan: $q$-Analogue of certain operational formulae.Houston J. Math. 13 (1987), no. 1, pp. 75–82. MR 0884235 |
| Reference:
|
[7] M. A. Khan: On a calculus for the $T_{k,q,x}$-operator.Mathematica Balkanica, New series 6 (1992), fasc. 1, pp. 83–90. MR 1170732 |
| Reference:
|
[8] M. A. Khan: On some operational representations of $q$-polynomials.Czechoslovak Mathematical Journal 45 (1995), 457–464. Zbl 0836.33009, MR 1344511 |
| Reference:
|
[9] M. A. Khan, A. H. Khan: On some characterizations of $q$-Bessel polynomials.Acta Math. Viet. 15 (1990), no. 1, pp. 55–59. MR 1087787 |
| Reference:
|
[10] H. B. Mittal: Some generating functions.Univ. Lisbova Revista Fae. Ci A(2). Mat. 13 (1970), 43–51. Zbl 0229.33015, MR 0308486 |
| Reference:
|
[11] E. D. Rainville: Special Functions.The MacMillan Co., New York (1960). Zbl 0092.06503, MR 0107725 |
| Reference:
|
[12] L. J. Slater: Generalized Hypergeometric Functions.Cambridge University Press (1966). Zbl 0135.28101, MR 0201688 |
| Reference:
|
[13] H. M. Srivastava, H. L. Manocha: A Treatise on Generating Functions.John Wiley and Sons (Halsted Press), New York, Ellis Horwood, Chichester, 1985. MR 0750112 |
| . |
