Densely generated 2D q-Appell polynomials of Bessel type and q-addition formulas
DOI:
https://doi.org/10.5269/bspm.46923Abstract
The article aims to introduce a densely generated class of $2D$ $q$-Appell polynomials of Bessel type via generating equation and to establish its $q$-determinant form. It is advantageous to consider the $2D$ $q$-Bernoulli, $2D$ $q$-Roger Szeg\"{o} and $2D$ $q$-Al-Salam Carlitz polynomials of Bessel type as their special members. The $q$-determinant forms and certain $q$-addition formulas are derived for these polynomials. The article concludes with a brief view on discrete $q$-Bessel convolution of the $2D$ $q$-Appell polynomials.
References
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2. Al-Salam, W. A., q-Bernoulli numbers and polynomials, Math. Nachr. 17, 239-260, (1959). https://doi.org/10.1002/mana.19580170311
3. Andrews, G.E., Askey, R., Roy, R., Special Functions, Encyclopedia of Mathematics and its Applications, Vol. 71, Cambridge University Press, Cambridge, London and New York, 1999.
4. Atakishiyev, N. M., Nagiyev, Sh. M., On the Roger-Szego polynomials, J. Phys. A: Math. Gen. 27, L611-L615, (1994). https://doi.org/10.1088/0305-4470/27/17/003
5. Carlitz, L., A note on the Bessel polynomials, Duke Math. J. 24, 151-162, (1957). https://doi.org/10.1215/S0012-7094-57-02421-3
6. Dattoli, G., Gainnnessi, L., Mezi, I., Torre, A., Theory of generalized Bessel functions, Nuovo Cimento, 105(3), 327-347, (1990). https://doi.org/10.1007/BF02726105
7. Eini Keleshteri, M., Mahmudov, N. I., A study on q-Appell polynomials from determinantal point of view, Appl. Math. Comput. 260 351-369, (2015). https://doi.org/10.1016/j.amc.2015.03.017
8. Koekoek, R., Lesky, P. A., Swarttouw, R. F., Hypergeometric orthogonal polynomials and their q-analogues, Springer, Berlin, (2010). https://doi.org/10.1007/978-3-642-05014-5
9. Mahmudov, N. I., On a class of q-Bernoulli and q-Euler polynomials, Adv. Difference Equ. 108, 1-11, (2013). https://doi.org/10.1186/1687-1847-2013-108
10. Riyasat, M. , Khan, S., A determinant approach to q-Bessel polynomials and applications, Racsam. https://doi.org/10.1007/s13398-018-0568-y
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Published
2022-02-02
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Funding data
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Department of Atomic Energy, Government of India
Grant numbers Office Memo No.2/40(38)/2016/R$\&$D-II/1063
