• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.417-445
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• 2020

The purpose of this article is to continue the study of q, 𝜔-special functions in the spirit of Wolfgang Hahn from the previous papers by Annaby et al. and Varma et al., with emphasis on q, 𝜔-Apostol Bernoulli and Euler polynomials, Ward-𝜔 numbers and multiple q, 𝜔power sums. Like before, the q, 𝜔-module for the alphabet of q, 𝜔-real numbers plays a crucial role, as well as the q, 𝜔-rational numbers and the Ward-𝜔 numbers. There are many more formulas of this type, and the deep symmetric structure of these formulas is described in detail.

• Communications of the Korean Mathematical Society
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• v.32 no.2
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• pp.305-319
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• 2017

Recently many authors have investigated so-called Aleph (${\aleph}$)-function and its various properties. Here, in this paper, we aim at establishing certain integral formulas involving the Aleph (${\aleph}$)-function. Precisely, integrals with product of Aleph (${\aleph}$)-function with Jacobi polynomials, Bessel Maitland function, general class of polynomials were under consideration. Some interesting special cases of our main result are also considered and shown to be connected with certain known ones.

• Communications of the Korean Mathematical Society
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• v.30 no.3
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• pp.191-200
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• 2015

Generating functions play an important role in the investigation of various useful properties of the sequences which they generate. Exton [13] presented a very general double generating relation involving products of two Laguerre polynomials. Motivated essentially by Exton's derivation [13], the authors aim to show how one can obtain nineteen new generating relations associated with products of two Laguerre polynomials in the form of a single result. We also consider some interesting and potentially useful special cases of our main findings.

• East Asian mathematical journal
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• v.34 no.3
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• pp.295-303
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• 2018

Gautam et al. [9] introduced the multivariable A-function, which is very general, reduces to yield a number of special functions, in particular, the multivariable H-function. Here, first, we aim to establish two very general integral formulas involving product of the general class of Srivastava multivariable polynomials and the multivariable A-function. Then, using those integrals, we find a solution of partial differential equations of heat conduction at zero temperature with radiation at the ends in medium without source of thermal energy. The results presented here, being very general, are also pointed out to yield a number of relatively simple results, one of which is demonstrated to be connected with a known solution of the above-mentioned equation.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.301-310
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• 2005

The coefficients of the Rudin-Shapiro polynomials are $\pm1$. In this paper we first replace-1 coefficient by 0 which on that case the structure of the coefficients will be on base 2. Then using the results obtained for the numbers on base 2, we introduce a quite fast algorithm to calculate the autocorrelation coefficients. Main facts: Regardless of frequencies, finding the autocorrelations of those polynomials on which their coefficients lie in the unit disk has been a telecommunication's demand. The Rudin-Shapiro polynomials have a very special form of coefficients that allow us to use 'Machine language' for evaluating these values.

• Coupled systems mechanics
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• v.6 no.4
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• pp.487-499
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• 2017

This paper investigates the approximate solution bounds of radon diffusion equation in soil pore matrix coupled with uncertainty. These problems have been modeled by few researchers by considering the parameters as crisp, which may not give the correct essence of the uncertainty. Here, the interval uncertainties are handled by parametric form and solution of the relevant uncertain diffusion equation is found by using Galerkin's Method. The shape functions are taken as the linear combination of orthogonal polynomials which are generated based on the parametric form of the interval uncertainty. Uncertain bounds are computed and results are compared in special cases viz. with the crisp solution.

• Honam Mathematical Journal
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• v.41 no.1
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• pp.135-152
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• 2019

In the last decades, various integral formulas associated with Bessel functions of different kinds as well as Bessel functions themselves, have been studied and a noteworthy amount of work can be found in the literature. Following up, we present two definite integral formulas involving the product of generalized Bessel function associated with orthogonal polynomials. Also, some intriguing special cases of our main results have been discussed.

• Honam Mathematical Journal
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• v.43 no.4
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• pp.597-612
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• 2021

Several useful and interesting extensions of the various special functions have been introduced by many authors during the last few decades. Various integral formulas associated with Wright function have been studied and a noteworthy amount of work have found in literature. The principal object of the present paper is to evaluate finite integral formulas containing the product of orthogonal polynomials with generalized Wright function. These integral formulas are expressed in terms of Srivastava and Daoust function. Some interesting particular cases are obtained from the main results by specialising the suitable values of the parameters involved.

• Journal for History of Mathematics
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• v.26 no.2_3
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• pp.149-161
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• 2013

The history of finding solutions of linear equations went back to some thousand years ago, and has been steadily developed to solve systems of higher degree polynomials. The method to eliminate variables came into use around the 17th and 18th century. This technique has been extended to the resultant theory that was laid in the 19th century by outstanding mathematicians as Euler, Sylvester, and B$\acute{e}$zout. In this paper we discuss the historical reflection about the development of solving system of polynomials. We add a special emphasis on E. B$\acute{e}$zout who gave the first account on the resultant which is a generalization of discriminant and Gauss elimination method.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.8
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• pp.1485-1492
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• 1992

While the vibration of circular plates were considered by many researchers, rather less attention is given to elliptical plates. In the present paper, the Rayleigh-Ritz mothod is used to obtain an eigenvalue equation for the free flexural vibration of thin elliptical plates having the classical free, simply suported or clmped boundary condition. Circular plates are included as a special case of the elliptical plates. Products of simple polynomials are used as the admissible functions and a recurrence relationship facilitates the evaluation of the necessary integrals. The analysis is developed for rectilinear orthotropic plates but the numerical results are given for isotropic plates with various aspect ratios.