• Journal of the Korean Mathematical Society
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• v.44 no.2
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• pp.487-498
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• 2007

In this paper, we obtain important combinatorial identities of generalized harmonic numbers using symmetric polynomials. We also obtain the matrix representation for the generalized harmonic numbers whose inverse matrix can be computed recursively.

• East Asian mathematical journal
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• v.11 no.1
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• pp.81-86
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• 1995

• 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 the Chungcheong Mathematical Society
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• v.26 no.3
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• pp.591-599
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• 2013

A large number of sequences of polynomials and numbers have arisen in mathematics. Some of them, for example, Bernoulli polynomials and numbers, have been investigated deeply and widely. Here we aim at presenting certain interesting and (potentially) useful identities involving mainly in the second-order Eulerian numbers and Stirling polynomials, which seem to have not been given so much attention.

• East Asian mathematical journal
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• v.32 no.1
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• pp.47-59
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• 2016

The purpose of the present paper is to introduce and investigate two new subclasses of bi-univalent functions of complex order defined in the open unit disk, which are associated with Hurwitz-Lerch zeta function and satisfying subordinate conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients ${\mid}a_2{\mid}$ and ${\mid}a_3{\mid}$ for functions in the new subclasses. Several (known or new) consequences of the results are also pointed out.

• Journal of the Korean Mathematical Society
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• v.55 no.5
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• pp.1207-1220
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• 2018

The generalized hyperharmonic numbers $h^{(m)}_n(k)$ are defined by means of the multiple harmonic numbers. We show that the hyperharmonic numbers $h^{(m)}_n(k)$ satisfy certain recurrence relation which allow us to write them in terms of classical harmonic numbers. Moreover, we prove that the Euler-type sums with hyperharmonic numbers: $$S(k,m;p):=\sum\limits_{n=1}^{{\infty}}\frac{h^{(m)}_n(k)}{n^p}(p{\geq}m+1,\;k=1,2,3)$$ can be expressed as a rational linear combination of products of Riemann zeta values and harmonic numbers. This is an extension of the results of Dil [10] and $Mez{\ddot{o}}$ [19]. Some interesting new consequences and illustrative examples are considered.

• Journal of the Korean Mathematical Society
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• v.40 no.6
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• pp.963-975
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• 2003

The aim of this work is to construct twisted q-L-series which interpolate twisted q-generalized Bernoulli numbers. By using generating function of q-Bernoulli numbers, twisted q-Bernoulli numbers and polynomials are defined. Some properties of this polynomials and numbers are described. The numbers $L_{q}(1-n,\;X,\;{\xi})$ is also given explicitly.

• Kyungpook Mathematical Journal
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• v.55 no.1
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• pp.29-39
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• 2015

In this paper, we investigate the functional equations of the multiple Dirichlet and Hurwitz L-functions associated with Bernoulli numbers and polynomials attached to Dirichlet character.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1573-1581
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• 2010

we investigate the n-fold convolution of the uniform distributions. First, we are concerned with the explicit distribution function of the partial sum ${\zeta}_n$ when the random variables are independent and has identically uniform distribution, next, we determine the n-fold convolution distribution of ${\zeta}_n$ when the identically distributed condition is not satisfied.

• Journal of applied mathematics & informatics
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• v.38 no.5_6
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• pp.611-623
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• 2020

In this paper, we define a q-analogue of the poly-Euler numbers and polynomials which is generalization of the poly Euler numbers and polynomials including q-analogue of polylogarithm function. We also give the relations between generalized poly-Euler polynomials. Furthermore, we introduce zeta fuctions of Arakawa-Kaneko type and talk their properties and the relation with q-analogue of poly-Euler polynomials.