Abstract:
Certain orthogonal polynomials are involved in various problems occurring in probability,
celestial mechanics, combinatorics, and other fields of theoretical and applied sciences.
The article aims to introduce
$q$-Sheffer sequences of Bessel type using
$q$-Riordan
matrices by means of the Eulerian generating function.
Series expansion and
determinant expressions are obtained for these
$q$-sequences.
We discuss the orthogonality
of
$q$-Sheffer sequences of Bessel type by establishing their three term
$q$-recurrence
relations.
As applications, we obtain the Eulerian generating functions and other
properties for some special
$q$-Sheffer sequences of Bessel type including the continuous
$q$-Hermite and
$q$-exponential polynomials of Bessel type.
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