A determinant approach to q-Bessel polynomials and applications

The article aims to introduce the q-analogues of well known Bessel polynomials and to study their important properties. A new recurrence relation and determinant definition for the q-Bessel polynomials are derived. A hybrid form of q-Bessel polynomials namely, the extended q-Eulerian type-Bessel polynomials are introduced and are characterized by means of series expansion and determinant definition. As an special case, the characterizations for the extended q-Euler–Bessel polynomials are given. Further, the 2Dq-Bessel polynomials are introduced by means of generating function and determinant definition and some identities for these q-polynomials are proved.