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

Volume 11, Issue 6, pp 785--797 http://dx.doi.org/10.22436/jnsa.011.06.06
Publication Date: April 25, 2018 Submission Date: June 28, 2017 Revision Date: January 16, 2017 Accteptance Date: March 08, 2018

Authors

Cheon Seoung Ryoo - Department of Mathematics, Hannam University, Daejeon 306-791, Republic of Korea. Kyung Won Hwang - Department of Mathematics, Dong-A University, Busan 604-714, Republic of Korea. Do Jin Kim - Department of Mathematics, Kyungpook National University, Daegu, 702-701, Republic of Korea. Nam Soon Jung - College of Talmage Liberal Arts, Hannam University,, Daejeon 306-791, Republic of Korea.


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.


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ISRP Style

Cheon Seoung Ryoo, Kyung Won Hwang, Do Jin Kim, Nam Soon Jung, Dynamics of the zeros of analytic continued polynomials and differential equations associated with \(q\)-tangent polynomials, Journal of Nonlinear Sciences and Applications, 11 (2018), no. 6, 785--797

AMA Style

Ryoo Cheon Seoung, Hwang Kyung Won, Kim Do Jin, Jung Nam Soon, Dynamics of the zeros of analytic continued polynomials and differential equations associated with \(q\)-tangent polynomials. J. Nonlinear Sci. Appl. (2018); 11(6):785--797

Chicago/Turabian Style

Ryoo, Cheon Seoung, Hwang, Kyung Won, Kim, Do Jin, Jung, Nam Soon. "Dynamics of the zeros of analytic continued polynomials and differential equations associated with \(q\)-tangent polynomials." Journal of Nonlinear Sciences and Applications, 11, no. 6 (2018): 785--797


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