• 대한수학회논문집
• /
• 제34권2호
• /
• pp.383-390
• /
• 2019

In this paper, we discuss special polynomials involving exponential distribution, which is related to life testing. We derive some identities of special polynomials such as the symmetric property, recurrence formula and so on. In addition, we investigate explicit properties of special polynomials by using their derivative and integral.

• Journal of applied mathematics & informatics
• /
• 제36권5_6호
• /
• pp.541-553
• /
• 2018

We introduce q-special numbers and polynomials with q-exponential distribution. From these numbers and polynomials we derive some properties and identites. We also find approximated zeros of q-special polynomials and investigate property of two parameters ${\lambda}$, q.

• Journal of applied mathematics & informatics
• /
• 제38권1_2호
• /
• pp.37-56
• /
• 2020

In this paper we discuss some interesting properties of (p, q)-special polynomials and derive various relations. We gain some relations between (p, q)-zeta function and (p, q)-special polynomials by considering (p, q)-analogue Euler sum types. In addition, we derive the relationship between (p, q)-polylogarithm function and (p, q)-special 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.

• 대한수학회논문집
• /
• 제36권1호
• /
• pp.19-26
• /
• 2021

Degenerate versions of the special polynomials and numbers since they have many applications in analytic number theory, combinatorial analysis and p-adic analysis. In this paper, we define the degenerate poly-Euler numbers and polynomials arising from the modified polyexponential functions. We derive explicit relations for these numbers and polynomials. Also, we obtain some identities involving these polynomials and some other special 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
• /
• 제34권3호
• /
• pp.311-326
• /
• 2012

The purpose of this paper is to introduce and investigate two new classes of generalized Bernoulli and Apostol-Bernoulli polynomials based on the definition given recently by the authors [29]. In particular, we obtain a new addition formula for the new class of the generalized Bernoulli polynomials. We also give an extension and some analogues of the Srivastava-Pint$\acute{e}$r addition theorem [28] for both classes. Finally, by making use of the new adition formula, we exhibit several interesting relationships between generalized Bernoulli polynomials and other polynomials or special functions.

• 조명전기설비학회논문지
• /
• 제16권2호
• /
• pp.98-103
• /
• 2002

전력수요를 예측할 경우 가장 중요한 문제 중의 하나가 특수일 부하의 처리문제이다. 따라서 본 연구에서 길고(구정, 추석) 짧은(식목일, 현충일 등) 특수일 피크 부하를 신경회로망과 회귀모형을 이용하여 예측하는 방법을 제시한다. 신경회로망 모형의 특수일 부하 처리는 패턴 변환비를 이용하며, 4차의 직교 다항 회귀모형은 과거의 10년 (1985∼1994)간의 특수일 피크부하 자료를 이용하여 길고 짧은 특수일 부하를 예측한다. 특수일 피크 부하를 예측한 결과, 신경회로망 모형의 주간 평균 예측 오차율과 직교 다항 회귀모형의 예측 오차율을 분석한 결과 1∼2[%]대로 두 모형 모두 양호한 결과를 얻었다. 또한 4차의 직교 다항 회귀 모형의 수정결정계수 및 F 검정을 분석한 결과 구성한 예측 모형의 타당성을 확인하였다. 두 모형의 특수일 부하를 예측한 결과를 비교해 보면 긴 특수일 부하를 예측할 때는 패턴 변환비를 이용한 신경회로망 모형이 보다 더 효과적이었고, 짧은 특수일 부하를 예측할 경우에는 두 방법 모두 유효하였다.

• 대한수학회논문집
• /
• 제31권4호
• /
• pp.827-844
• /
• 2016

Here, in this paper, we aim at establishing some new unified integral and differential formulas associated with the $\bar{H}$-function. Each of these formula involves a product of the $\bar{H}$-function and Srivastava polynomials with essentially arbitrary coefficients and the results are obtained in terms of two variables $\bar{H}$-function. By assigning suitably special values to these coefficients, the main results can be reduced to the corresponding integral formulas involving the classical orthogonal polynomials including, for example, Hermite, Jacobi, Legendre and Laguerre polynomials. Furthermore, the $\bar{H}$-function occurring in each of main results can be reduced, under various special cases.

• Journal of applied mathematics & informatics
• /
• 제39권1_2호
• /
• pp.83-91
• /
• 2021

In this paper, we introduce the concepts of q-cosine tangent polynomials and q-sine tangent polynomials. From these polynomials, we find some identities and properties by using q-numbers and q-trigonometric functions.