| Title:
|
On some operational representations of $q$-polynomials (English) |
| Author:
|
Khan, Mumtaz Ahmad |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
45 |
| Issue:
|
3 |
| Year:
|
1995 |
| Pages:
|
457-464 |
| . |
| Category:
|
math |
| . |
| MSC:
|
33D45 |
| MSC:
|
33D60 |
| MSC:
|
39A10 |
| idZBL:
|
Zbl 0836.33009 |
| idMR:
|
MR1344511 |
| DOI:
|
10.21136/CMJ.1995.128538 |
| . |
| Date available:
|
2009-09-24T09:49:16Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128538 |
| . |
| Reference:
|
[1] W.H. Abidi: A basic analogue of the Bessel polynomials.Math. Nachr. 30 (1965), 209–219. MR 0190382, 10.1002/mana.19650300308 |
| Reference:
|
[2] R.P. Agarwal and A. Verma: Generalized basic hypergeometric series with unconnected bases.Proc. Camb. Philos. Soc. 63 (1967), 727–734. MR 0212216, 10.1017/S0305004100041724 |
| Reference:
|
[3] N.A. Al-Salam: Some operational formulas for the $q$-Laguerre polynomials.Fibonacci Quaterly 22 (1984), 166–170. Zbl 0537.33006, MR 0742847 |
| Reference:
|
[4] N.A. Al-Salam: On some $q$-operators with applications.Proc. Konen. Nederl. Akademicvan Wetenschappen, Ser. A 92 (1989), 1–13. Zbl 0696.47046, MR 0993673 |
| Reference:
|
[5] W.A. Al-Salam: Operational representation for the Laguerre and Hermite polynomials.Duke Math. Journal 31 (1964), 127–142. MR 0159053 |
| Reference:
|
[6] W.A. Al-Salam and A. Verma: Orthogonality Preserving Operators.I. Atti Della Academia Nazionale Dei Lincei, ser VIII Vol. 2 VIII (1975), 833–838. MR 0440090 |
| Reference:
|
[7] W.A. Al-Salam and L. Carlitz: Some orthogonal $q$-polynomials.Math. Nachr. 30 (1965), 47–61. MR 0197804, 10.1002/mana.19650300105 |
| Reference:
|
[8] H. Exton: $q$-Hypergeometric Functions and Applications.John Wiley and Sons (Halsted Press), New York — Ellis Horwood, Chichester, 1983. Zbl 0514.33001, MR 0708496 |
| Reference:
|
[9] W. Hahn: Beiträge zur Theorie der Heinschen Reihen, Die 24 Integrale der hypergeometrischen $q$-Differenzengleichung, Das $q$-Analogen der Laplace Transformation.Math. Nachr.. MR 0035344 |
| Reference:
|
[10] W. Hahn: $q$-Differenzengleichung, Das $q$-Analogen der Laplace Transformation.Math. Nachr. 2 (1949). MR 0035344 |
| Reference:
|
[11] M.E.H. Ismail: The zeros of basic Bessel functions, the functions $J_{v+ax}(x)$ and associated orthogonal polynomials.J. Math. Anal. Appl. 86 (1982), no. 1, 1–19. MR 0649849, 10.1016/0022-247X(82)90248-7 |
| Reference:
|
[12] F.H. Jackson: Basic double hypergeometric functions.Quart. J. Math. (Oxford) 15 (1944), 49–61. Zbl 0060.19810, MR 0011348, 10.1093/qmath/os-15.1.49 |
| Reference:
|
[13] M.A. Khan: Certain fractional $q$-integrals and $q$-derivatives.Nanta Mathematica 7 (1974), no. 1, 52–60. Zbl 0289.33009, MR 0369630 |
| Reference:
|
[14] M.A. Khan: On $q$-Laguerre polynomials.Ganita 34 (1983), no. 1 and 2, 111–123. Zbl 0638.33006, MR 0910619 |
| Reference:
|
[15] M.A. Khan: $q$-Analogue of certain operational formulae.Houston J. Math. 13 (1987), no. 1, 75–82. MR 0884235 |
| Reference:
|
[16] M.A. Khan: On a calculus for the $T_{k,q,x}$-operator.Mathematica Balkanica, New Series 6 (1992), no. 1, 83–90. MR 1170732 |
| Reference:
|
[17] M.A. Khan and A.H. Khan: Fractional $q$-integration and integral representations of ‘Bibasic’ double hypergeometric series of higher order.Acta Mathematica Vietnamica 11 (1986), no. 2, 234–240. MR 0882584 |
| Reference:
|
[18] M.A. Khan and A.H. Khan: On some characterizations of $q$-Bessel polynomials.Acta Math. Viet. 15 (1990), no. 1, 55–59. MR 1087787 |
| Reference:
|
[19] H.B. Mittal: Operational representation for the generalized Laguerre polynomials.Glasnik Mathematički 6(26) (1977), no. 1, 45–53. MR 0299847 |
| Reference:
|
[20] E.D. Rainville: Special Functions.The MacMillan Co., New York, 1960. Zbl 0092.06503, MR 0107725 |
| Reference:
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[21] L.J. Slater: Generalized Hypergeometric Functions.Cambridge University Press, 1966. Zbl 0135.28101, MR 0201688 |
| Reference:
|
[22] H.M. Srivastava and H.L. Manocha: A Treatise on Generating Functions.John Wiley and Sons (Halsted Press), New York; Ellis Horwood, Chichester, 1984. MR 0750112 |
| . |
