• Title/Summary/Keyword: special polynomials

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SOME PROPERTIES OF SPECIAL POLYNOMIALS WITH EXPONENTIAL DISTRIBUTION

  • Kang, Jung Yoog;Lee, Tai Sup
    • Communications of the Korean Mathematical Society
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    • v.34 no.2
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    • pp.383-390
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    • 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.

SOME EXPLICIT PROPERTIES OF (p, q)-ANALOGUE EULER SUM USING (p, q)-SPECIAL POLYNOMIALS

  • KANG, J.Y.
    • Journal of applied mathematics & informatics
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    • v.38 no.1_2
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    • pp.37-56
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    • 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.

ON THE SPECIAL VALUES OF TORNHEIM'S MULTIPLE SERIES

  • KIM, MIN-SOO
    • Journal of applied mathematics & informatics
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    • v.33 no.3_4
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    • pp.305-315
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    • 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.

DEGENERATE POLYEXPONENTIAL FUNCTIONS AND POLY-EULER POLYNOMIALS

  • Kurt, Burak
    • Communications of the Korean Mathematical Society
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    • v.36 no.1
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    • pp.19-26
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    • 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.

A RESEARCH ON THE GENERALIZED POLY-BERNOULLI POLYNOMIALS WITH VARIABLE a

  • JUNG, Nam-Soon;RYOO, Cheon Seoung
    • Journal of applied mathematics & informatics
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    • v.36 no.5_6
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    • pp.475-489
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    • 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.

A FURTHER GENERALIZATION OF APOSTOL-BERNOULLI POLYNOMIALS AND RELATED POLYNOMIALS

  • Tremblay, R.;Gaboury, S.;Fugere, J.
    • Honam Mathematical Journal
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    • v.34 no.3
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    • pp.311-326
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    • 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.

Special-Days Load Handling Method using Neural Networks and Regression Models (신경회로망과 회귀모형을 이용한 특수일 부하 처리 기법)

  • 고희석;이세훈;이충식
    • Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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    • v.16 no.2
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    • pp.98-103
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    • 2002
  • In case of power demand forecasting, the most important problems are to deal with the load of special-days. Accordingly, this paper presents the method that forecasting long (the Lunar New Year, the Full Moon Festival) and short(the Planting Trees Day, the Memorial Day, etc) special-days peak load using neural networks and regression models. long and short special-days peak load forecast by neural networks models uses pattern conversion ratio and four-order orthogonal polynomials regression models. There are using that special-days peak load data during ten years(1985∼1994). In the result of special-days peak load forecasting, forecasting % error shows good results as about 1 ∼2[%] both neural networks models and four-order orthogonal polynomials regression models. Besides, from the result of analysis of adjusted coefficient of determination and F-test, the significance of the are convinced four-order orthogonal polynomials regression models. When the neural networks models are compared with the four-order orthogonal polynomials regression models at a view of the results of special-days peak load forecasting, the neural networks models which uses pattern conversion ratio are more effective on forecasting long special-days peak load. On the other hand, in case of forecasting short special-days peak load, both are valid.

FRACTIONAL CALCULUS FORMULAS INVOLVING $\bar{H}$-FUNCTION AND SRIVASTAVA POLYNOMIALS

  • Kumar, Dinesh
    • Communications of the Korean Mathematical Society
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    • v.31 no.4
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    • pp.827-844
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    • 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.