• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.35 no.7
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• pp.586-591
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• 2007

The effects of cancellation errors on the convergence characteristics of preconditioned Euler equations at low Mach numbers are analyzed. Flows in a two-dimensional channel with a circular bump are calculated at different Mach numbers. It is shown that the cancellation error in the energy equation grows faster than those in the other equations as the Mach number decreases. It is also shown that the cancellation problem of the energy equation can be alleviated by multiplying the inversion of the preconditioner.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.511-516
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• 2011

In this paper we prove a generalized symmetry relation between the generalized Euler polynomials and the generalized higher-order (attached to Dirichlet character) Euler polynomials. Indeed, we prove a relation between the power sum polynomials and the generalized higher-order Euler polynomials..

• Honam Mathematical Journal
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• v.46 no.2
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• pp.168-180
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• 2024

The main object of this article is to propose a unified extension of Bernoulli, Euler and Genocchi polynomials by means of a new family of mixed polynomials whose generating function is given in terms of generalized Bessel function. We also discuss here some fundamental properties of our introduced mixed polynomials by making use of the series arrangement technique. Furthermore, some conclusions of our present study are also pointed out in the last section.

• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.337-346
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• 2012

In this paper we construct a new type of twisted $q$-Genocchi numbers $G_{n,q,w}^{({\alpha})}$ and polynomials $G_{n,q,w}^{({\alpha})}(x)$. Some interesting results and relationships are obtained.

• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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• pp.933-955
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• 2023

For any prime number p, let J(p) be the set of positive integers n such that the numerator of the n^th harmonic number in the lowest terms is divisible by this prime number p. We consider an extension of this set to the generalized harmonic numbers, which are a natural extension of the harmonic numbers. Then, we present an upper bound for the number of elements in this set. Moreover, we state an explicit condition to show the finiteness of our set, together with relations to Bernoulli and Euler numbers.

• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.671-697
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• 2024

In this paper, we formally introduce the notion of a general parametric digamma function Ψ(−s; A, a) and we find the Laurent expansion of Ψ(−s; A, a) at the integers and poles. Considering the contour integrations involving Ψ(−s; A, a), we present some new identities for infinite series involving Dirichlet type parametric harmonic numbers by using the method of residue computation. Then applying these formulas obtained, we establish some explicit relations of parametric linear Euler sums and some special functions (e.g. trigonometric functions, digamma functions, Hurwitz zeta functions etc.). Moreover, some illustrative special cases as well as immediate consequences of the main results are also considered.

• Bulletin of the Korean Mathematical Society
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• v.43 no.3
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• pp.611-617
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• 2006

In this paper we construct q-Genocchi numbers and polynomials. By using these numbers and polynomials, we investigate the q-analogue of alternating sums of powers of consecutive integers due to Euler.

• Honam Mathematical Journal
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• v.35 no.2
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• pp.137-146
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• 2013

Motivated essentially by their potential for applications in a wide range of mathematical and physical problems, the log-sine and log-cosine integrals have been evaluated, in the existing literature on the subject, in many different ways. The main object of this paper is to present explicit evaluations of some families of log-sine and log-cosine integrals by making use of the familiar Beta function.

• Communications of the Korean Mathematical Society
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• v.29 no.2
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• pp.239-255
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• 2014

We develop a set of identities for Euler type sums. In particular we investigate products of shifted harmonic numbers of order two and reciprocal binomial coefficients.

• East Asian mathematical journal
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• v.16 no.2
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• pp.233-237
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• 2000

Since the time of Euler, there have been many proofs giving the value of $\zeta(2n)$. We also give an evaluation of $\zeta(2n)$ by analyzing the generating function of Bernoulli numbers.