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

Volume 11, Issue 6, pp 785--797
Publication Date: April 25, 2018 Submission Date: June 28, 2017 Revision Date: January 16, 2017 Accteptance Date: March 08, 2018
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### 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.

### Share and Cite

##### 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

### Keywords

• Tangent numbers and polynomials
• $q$-tangent polynomial
• $q$-tangent Zeta function
• analytic continuation
• analytic continued $q$-tangent polynomials
• zeros
• differential equations

•  11B68
•  11S40

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