• Kyungpook Mathematical Journal
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• v.57 no.2
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• pp.233-244
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• 2017

Differential subordination and superordination results associated with a generalized Hurwitz-Lerch Zeta function in the open unit disk are obtained by investigating appropriate classes of admissible functions. In particular some inequalities for generalized Hurwitz-Lerch Zeta function are obtained.

• Journal of applied mathematics & informatics
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• v.36 no.5_6
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• pp.555-565
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• 2018

The main subject of this paper is to introduce the (p, q)-Euler polynomials and obtain several interesting symmetric properties of the modified (p, q)-Hurwitz Euler Zeta function with regard to (p, q) Euler polynomials. In order to get symmetric properties, we introduce the new (p, q)-analogue of Euler polynomials $E_{n,p,q}(x)$ and numbers $E_{n,p,q}$.

• Journal of the Korean Mathematical Society
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• v.57 no.6
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• pp.1535-1549
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• 2020

This paper deals with the inverse of tails of Hurwitz zeta function. More precisely, for any positive integer s ≥ 2 and 0 ≤ a < 1, we give an algorithm for finding a simple form of f_s,a(n) such that $$\lim_{n{\rightarrow}{\infty}}\{\({\sum\limits_{k=n}^{\infty}}{\frac{1}{(k+a)^s}}\)^{-1}-f_{s,a}(n)\}=0$$. We show that f_s,a(n) is a polynomial in n-a of order s-1. All coefficients of f_s,a(n) are represented in terms of Bernoulli numbers.

• Honam Mathematical Journal
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• v.39 no.4
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• pp.561-568
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• 2017

Hurwitz zeta function occurs in various parts of mathematics. In particular, it plays an important role in some area of number theory. In this paper, using a certain transformation formula, we find some identities of relations between ${\zeta}(2n+1)$ and ${\zeta}(2n+1,{\alpha})$ for special values of ${\alpha}$.

• East Asian mathematical journal
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• v.18 no.2
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• pp.219-224
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• 2002

Recently the theory of the multiple Gamma functions, which were studied by Barnes and others a century ago, has been revived in the study of determinants of Laplacians. Here we are aiming at evaluating the values of the multiple Gamma functions ${\Gamma}_n(\frac{1}{2})$ in terms of the Hurwitz or Riemann Zeta functions.

• Communications of the Korean Mathematical Society
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• v.31 no.2
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• pp.329-342
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• 2016

Motivated essentially by Brychkov's work [1], we evaluate some new integrals involving hypergeometric function and the logarithmic function (including those obtained by Brychkov[1], Choi and Rathie [3]), which are expressed explicitly in terms of Gamma, Psi and Hurwitz zeta functions suitable for numerical computations.

• Journal of applied mathematics & informatics
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• v.39 no.3_4
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• pp.455-467
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• 2021

In this paper, we define twisted q-Euler polynomials of the second kind and explore some properties. We find generating function of twisted q-Euler polynomials of the second kind. Also, we investigate twisted q-Raabe's multiplication formula and (w, q)-alternating power sums of twisted q-Euler polynomials of the second kind. At the end, we define twisted q-Hurwitz's type Euler zeta function of the second kind.

• 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.

• Korean Journal of Mathematics
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• v.19 no.2
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• pp.129-147
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• 2011

In this paper we discuss the zeta-determinants of harmonic oscillators having general quadratic potentials defined on $\mathbb{R}^2$. By using change of variables we reduce the harmonic oscillators having general quadratic potentials to the standard harmonic oscillators and compute their spectra and eigenfunctions. We then discuss their zeta functions and zeta-determinants. In some special cases we compute the zeta-determinants of harmonic oscillators concretely by using the Riemann zeta function, Hurwitz zeta function and Gamma function.

• Honam Mathematical Journal
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• v.35 no.4
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• pp.639-645
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• 2013

We aim at presenting certain integral representations for the Riemann Zeta function ${\zeta}(s)$ at positive integer arguments by using some known integral representations of log ${\Gamma}(1+z)$ and ${\psi}(1+z)$.