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