Affiliation:
1. Aligarh Muslim University
Abstract
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.
Publisher
Sociedade Paranaense de Matematica
Reference10 articles.
1. Al-Salam, W. A., q-Appell polynomials, Ann. Mat. Pura Appl. 4(17), 31-45, (1967). https://doi.org/10.1007/BF02416939
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