Dynamics of the zeros of analytic continued polynomials and differential equations associated with q-tangent polynomials

Abstract

In this paper, we study the analytic continuation T q (s) and T q (s, w) of the q-Tangent numbers T n,q and q-Tangent polynomials T n,q (x) introduced by authors. The new concept of dynamics of the zeros of analytic continued q-tangent polynomials is investigated observing an interesting phenomenon of 'scattering' of the zeros of T q (s, w). Finally, we study linear differential equations arising from the generating functions of q-tangent polynomials giving explicit identities for the q-tangent polynomials.