• Journal of applied mathematics & informatics
• /
• 제35권5_6호
• /
• pp.495-504
• /
• 2017

In this paper we construct the Carlitz's type q-tangent numbers $T_{n,q}$ and polynomials $T_{n,q}(x)$. From these numbers and polynomials, we establish some interesting identities and relations.

• Journal of applied mathematics & informatics
• /
• 제35권5_6호
• /
• pp.599-609
• /
• 2017

We construct degenerated Euler polynomials of the second kind and find some basic properties of this polynomials. From this paper, we can see degenerated alternative power sum is defined and is related to degenerated Euler polynomials of the second kind. Using this power sum, we have a number of symmetric properties of degenerated Euler polynomials of the second kind.

• Korean Journal of Mathematics
• /
• 제19권3호
• /
• pp.263-272
• /
• 2011

In the paper [1], an explicit correspondence between certain cubic irreducible polynomials over $\mathbb{F}_q$ and cubic irreducible polynomials of special type over $\mathbb{F}_{q^2}$ was established. In this paper, we show that we can mimic such a correspondence for quintic polynomials. Our transformations are rather constructive so that it can be used to generate irreducible polynomials in one of the finite fields, by using certain irreducible polynomials given in the other field.

• 호남수학학술지
• /
• 제39권2호
• /
• pp.259-265
• /
• 2017

Galois polynomials are defined as a generalization of the Cyclotomic polynomials. Galois polynomials have integer coefficients as the cyclotomic polynomials. But they are not always irreducible. In this paper, Galois polynomials are partly classified according to the type of subgroups which defines the Galois polynomial.

• 제어로봇시스템학회논문지
• /
• 제15권7호
• /
• pp.671-674
• /
• 2009

Determining the Schur stability of a polynomial is one of fundamental steps in many engineering problems including digital control system design or digital filter design. Due to its importance a variety of techniques have been reported in the literature for checking the Schur stability of a given polynomial. However most of them focus on real polynomials, and few results are available for complex polynomials. This paper concerns the Schur stability of complex polynomials. A simplified Jury's table for real polynomials is extended to complex polynomials.

• Journal of applied mathematics & informatics
• /
• 제33권3_4호
• /
• pp.305-315
• /
• 2015

Recently, Jianxin Liu, Hao Pan and Yong Zhang in [On the integral of the product of the Appell polynomials, Integral Transforms Spec. Funct. 25 (2014), no. 9, 680-685] established an explicit formula for the integral of the product of several Appell polynomials. Their work generalizes all the known results by previous authors on the integral of the product of Bernoulli and Euler polynomials. In this note, by using a special case of their formula for Euler polynomials, we shall provide several reciprocity relations between the special values of Tornheim's multiple series.

• 호남수학학술지
• /
• 제41권4호
• /
• pp.781-798
• /
• 2019

This paper is designed to introduce a Hermite-based-poly-Bernoulli numbers and polynomials with q-parameter. By making use of their generating functions, we derive several summation formulae, identities and some properties that is connected with the Stirling numbers of the second kind. Furthermore, we derive symmetric identities for Hermite-based-poly-Bernoulli polynomials with q-parameter by using generating functions.

• Journal of applied mathematics & informatics
• /
• 제35권1_2호
• /
• pp.113-120
• /
• 2017

In this paper, we introduce degenerate tangent numbers ${\mathcal{T}}^{(k)}_{n,q}({\lambda})$ and tangent polynomials ${\mathcal{T}}^{(k)}_{n,q}(x,{\lambda})$ of higher order. Finally, we obtain interesting properties of these numbers and polynomials.

• Journal of applied mathematics & informatics
• /
• 제36권5_6호
• /
• pp.475-489
• /
• 2018

In this paper, by using the polylogarithm function, we introduce a generalized poly-Bernoulli numbers and polynomials with variable a. We find several combinatorial identities and properties of the polynomials. We give some properties that is connected with the Stirling numbers of second kind. Symmetric properties can be proved by new configured special functions. We display the zeros of the generalized poly-Bernoulli polynomials with variable a and investigate their structure.

• 호남수학학술지
• /
• 제33권3호
• /
• pp.311-320
• /
• 2011

We in this paper construct Dirichlet's type twisted q-Euler numbers and polynomials with weight ${\alpha}$. We give some interestin identities some relations.