• Bulletin of the Korean Mathematical Society
• /
• v.47 no.3
• /
• pp.443-454
• /
• 2010

In this paper, we investigate the zeros distribution and Borel direction for the solutions of linear homogeneous differential equation $f^{(n)}+A_{n-2}(z)f^{(n-2)}+{\cdots}+A_1(z)f'+A_0(z)f=0(n{\geq}2)$ in an angular domain. Especially, we establish a relation between a cluster ray of zeros and Borel direction.

• Journal of the Korean Mathematical Society
• /
• v.59 no.3
• /
• pp.449-468
• /
• 2022

In this paper we determine explicitly the kernels 𝕜_α,β associated with new Bergman spaces A²_α,β(𝔻) considered recently by the first author and M. Zaway. Then we study the distribution of the zeros of these kernels essentially when α ∈ ℕ where the zeros are given by the zeros of a real polynomial Q_α,β. Some numerical results are given throughout the paper.

• Journal of Applied and Pure Mathematics
• /
• v.5 no.5_6
• /
• pp.291-301
• /
• 2023

In this paper, we investigate the zeros of the fully modified q-poly-tangent polynomials of the first type.

• Korean Journal of Mathematics
• /
• v.30 no.3
• /
• pp.503-512
• /
• 2022

In this paper, we are concerned with the problem of locating the zeros of regular polynomials of a quaternionic variable with quaternionic coefficients. We derive new bounds of Eneström-Kakeya type for the zeros of these polynomials by virtue of a maximum modulus theorem and the structure of the zero sets in the newly developed theory of regular functions and polynomials of a quaternionic variable. Our results generalize some recently proved results about the distribution of zeros of a quaternionic polynomial.

• Journal of Applied and Pure Mathematics
• /
• v.4 no.3_4
• /
• pp.123-139
• /
• 2022

In this paper we give some interesting properties of the cosine tangent polynomials and sine tangent polynomials. In addition, we give some identities for these polynomials and the distribution of zeros of these polynomials.

• The Pure and Applied Mathematics
• /
• v.24 no.2
• /
• pp.69-77
• /
• 2017

If q(z) is a polynomial of degree n with all zeros in the unit circle, then the self-reciprocal polynomial $q(z)+x^nq(1/z)$ has all its zeros on the unit circle. One might naturally ask: where are the zeros of $q(z)+x^nq(1/z)$ located if q(z) has different zero distribution from the unit circle? In this paper, we study this question when $q(z)=(z-1)^{n-k}(z-1-c_1){\cdots}(z-1-c_k)+(z+1)^{n-k}(z+1+c_1){\cdots}(z+1+c_k)$, where $c_j$ > 0 for each j, and q(z) is a 'zeros dragged' polynomial from $(z-1)^n+(z+1)^n$ whose all zeros lie on the imaginary axis.

• Journal of the Korean Mathematical Society
• /
• v.44 no.6
• /
• pp.1329-1338
• /
• 2007

In this paper, we study the location of zeros and Borel direction for the solutions of linear homogeneous differential equations $$f^{(n)}+A_{n-1}(z)f^{(n-1)}+{\cdots}+A_1(z)f#+A_0(z)f=0$$ with entire coefficients. Results are obtained concerning the rays near which the exponent of convergence of zeros of the solutions attains its Borel direction. This paper extends previous results due to S. J. Wu and other authors.

• Bulletin of the Korean Mathematical Society
• /
• v.47 no.6
• /
• pp.1189-1194
• /
• 2010

Kim and Park investigated the distribution of zeros around the unit circle of real self-reciprocal polynomials of even degrees with five terms, where the absolute value of middle coefficient equals the sum of all other coefficients. In this paper, we extend some of their results to the same kinds of polynomials with arbitrary many nonzero terms.

• Bulletin of the Korean Mathematical Society
• /
• v.51 no.2
• /
• pp.547-553
• /
• 2014

The Boubaker polynomials arose from the discretization of the equations of heat transfer in pyrolysis starting from an assumed solution of the form $$\frac{1}{N}e^{\frac{A}{H/z+1}}\sum_{k=0}^{\infty}{\xi}_kJ_k(t),$$ where $J_k$ is the k-th order Bessel function of the first kind. In this paper, we investigate the distribution of zeros of the Boubaker polynomials.

• Journal of Applied and Pure Mathematics
• /
• v.5 no.5_6
• /
• pp.375-387
• /
• 2023

In this paper, we construct a fully modified q-poly-Euler numbers and polynomials of the second type and give some properties. Finally, we investigate the zeros of the fully modified q-poly-Euler numbers and polynomials of the second type by using computer.