%0 Journal Article %T Dynamics of the zeros of analytic continued polynomials and differential equations associated with \(q\)-tangent polynomials %A Ryoo, Cheon Seoung %A Hwang, Kyung Won %A Kim, Do Jin %A Jung, Nam Soon %J Journal of Nonlinear Sciences and Applications %D 2018 %V 11 %N 6 %@ ISSN 2008-1901 %F Ryoo2018 %X 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. %9 journal article %R 10.22436/jnsa.011.06.06 %U http://dx.doi.org/10.22436/jnsa.011.06.06 %P 785--797