Open AccessDensely generated 2D q-Appell polynomials of Bessel type and q-addition formulas
Author(s) -
Mumtaz Riyasat
Publication year - 2022
Publication title -
boletim da sociedade paranaense de matemática
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.347
H-Index - 15
eISSN - 2175-1188
pISSN - 0037-8712
DOI - 10.5269/bspm.46923
Subject(s) - mathematics , bessel function , type (biology) , bessel polynomials , convolution (computer science) , pure mathematics , difference polynomials , wilson polynomials , orthogonal polynomials , discrete orthogonal polynomials , algebra over a field , mathematical analysis , computer science , ecology , machine learning , artificial neural network , biology
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.