Abstract
The intended objective of this study is to define and investigate a new class of q-generalized tangent-based Appell polynomials by combining the families of 2-variable q-generalized tangent polynomials and q-Appell polynomials. The investigation includes derivations of generating functions, series definitions, and several important properties and identities of the hybrid q-special polynomials. Further, the analogous study for the members of this q-hybrid family are illustrated. The graphical representation of its members is shown, and the distributions of zeros are displayed.
Highlights
Introduction and PreliminariesThe area of q-calculus in the last three decades act as a bridge between engineering sciences and mathematics
Research in the area of q-calculus has shown worthy of attention due to its applicative diversification in various fields such as mathematics, physics, and engineering
Using the expansion expressed in Equation (5) in the generating function expressed in Equation (13) of q-Appell polynomials and replacing powers of u ie u0, u1, u2, · · ·, un by the corresponding q-generalized tangent polynomials (qGTP) C0,m,q (u, v), C1,m,q (u, v), C2,m,q (u, v), · · ·, Cn,m,q (u, v) and thereafter using the generating function expressed in Equation (11) of qGTP Cn,m,q (u, v) and denoting the resultant (m) q-generalized tangent-based Appell polynomials by C An,q (u, v), the following definition is obtained: (m)
Summary
Introduction and PreliminariesThe area of q-calculus in the last three decades act as a bridge between engineering sciences and mathematics. We introduce the q-generalized tangent-based Appell polynomials (qGTAP) by means of a generating function. Utilizing generating function of q-Appell numbers and the relation expressed in Equation (11) in the generating function expressed in Equation (18) and employing the Cauchy product rule in the resultant expression and thereafter simplifying and comparing the coefficients of similar powers of t in (m) the resultant equation, we obtain the following series expansion of qGTAP C An,q (u, v): (m)
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