• Journal of applied mathematics & informatics
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• v.32 no.3_4
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• pp.465-474
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• 2014

Many mathematicians have studied various relations beween Euler number $E_n$, Bernoulli number $B_n$ and Genocchi number $G_n$ (see [1-18]). They have found numerous important applications in number theory. Howard, T.Agoh, S.-H.Rim have studied Genocchi numbers, Bernoulli numbers, Euler numbers and polynomials of these numbers [1,5,9,15]. T.Kim, M.Cenkci, C.S.Ryoo, L. Jang have studied the q-extension of Euler and Genocchi numbers and polynomials [6,8,10,11,14,17]. In this paper, our aim is introducing and investigating an extension term of generalized Euler polynomials. We also obtain some identities and relations involving the Euler numbers and the Euler polynomials, the Genocchi numbers and Genocchi polynomials.

• School Mathematics
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• v.12 no.4
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• pp.619-638
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• 2010

In this paper, we listed and reviewed some properties on polygonal numbers, pyramidal numbers and Pascal's triangle, and Fibonacci sequence. We discussed that the properties of gnomonic numbers, polygonal numbers and pyramidal numbers are explained integratively by introducing the generalized k-dimensional pyramidal numbers. And we also discussed that the properties of those numbers and relationships among generalized k-dimensional pyramidal numbers, Pascal's triangle and Fibonacci sequence are suitable for teaching and learning of mathematical reasoning and connections.

• Honam Mathematical Journal
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• v.35 no.3
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• pp.373-379
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• 2013

In contrast with numerous identities involving the binomial coefficients and the Stirling numbers of the first and second kinds, a few identities involving the Eulerian numbers have been known. The objective of this note is to present certain interesting and (presumably) new identities involving the Eulerian numbers by mainly making use of Worpitzky's identity.

• Journal of applied mathematics & informatics
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• v.35 no.5_6
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• pp.495-504
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• 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 the Korean Mathematical Society
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• v.56 no.2
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• pp.485-505
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• 2019

In 1935, D. H. Lehmer introduced and investigated generalized Euler numbers $W_n$, defined by $${\frac{3}{e^t+e^{wt}e^{w^2t}}}={\sum\limits_{n=0}^{\infty}}W_n{\frac{t^n}{n!}}$$, where ${\omega}$ is a complex root of $x^2+x+1=0$. In 1875, Glaisher gave several interesting determinant expressions of numbers, including Bernoulli and Euler numbers. These concepts can be generalized to the hypergeometric Bernoulli and Euler numbers by several authors, including Ohno and the second author. In this paper, we study more general numbers in terms of determinants, which involve Bernoulli, Euler and Lehmer's generalized Euler numbers. The motivations and backgrounds of the definition are in an operator related to Graph theory. We also give several expressions and identities by Trudi's and inversion formulae.

• Kyungpook Mathematical Journal
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• v.18 no.1
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• pp.31-36
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• 1978

This paper studies some problems suggested by Stirling numbers, and defines generalized Stirling numbers s(n, k, r), S(n, k, r) and proves that generalized Stirling numbers and certain linear combination of generalized Stirling numbers are strong logarithmic concave functions of k for fixed n and r.

• Journal of the Korean Mathematical Society
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• v.37 no.3
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• pp.391-410
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• 2000

In the complex case, we construct a q-analogue of the Riemann zeta function q(s) and a q-analogue of the Dirichlet L-function L(s,X), which interpolate the 1-analogue Bernoulli numbers. Using the properties of p-adic integrals and measures, we show that Kummer type congruences for the q-analogue Bernoulli numbers are the generalizations of the usual Kummer congruences for the ordinary Bernoulli numbers. We also construct a q0analogue of the p-adic L-function Lp(s, X;q) which interpolates the q-analogue Bernoulli numbers at non positive integers.

• Honam Mathematical Journal
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• v.33 no.3
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• pp.311-320
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• 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.

• Journal of the korean Society of Automotive Engineers
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• v.10 no.1
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• pp.26-32
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• 1988

A study has been conducted experimentally on the natural convection heat transfer characteristics of fin arrays on a horizontal flat plate in air. The effects of fin heights and Rayleigh numbers are mainly investigated. The experimental results are as follows; 1. The mean fin and mean total Nusselt numbers increase as dimensionless fin heights increase at 0.67.leg.H/s.leg.1.67. The mean plate Nusselt numbers increase in case of upward facing fins, but they decrease in case of downward facing fins. 2. The mean Nusselt numbers increase as Rayleigh numbers increase. 3. The mean fin surface Nusselt numbers has its maximum outside surface (Y$_{1}$) where there is no interference from each other fin. 4. The mean total Nusselt numbers in case of upward facing fins increase by 47% and 26%, respectively at H/S=0.67 and 1.67 than those in case of downward facing fins for Ra$_{s}$=6.50*10$^{3}$.>.

• Journal of applied mathematics & informatics
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• v.36 no.1_2
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• pp.115-120
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• 2018

In this paper, we discover symmetric properties for generalized Carlitz's q-tangent polynomials.