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Integral transforms and special functions, ISSN 1476-8291, 2018, Volume 30, Issue 4, pp. 282 - 300
Let p,x be real numbers, and s be a complex number, with , , and x+1>0. The zeta function is defined by where is a r-tuple positive integers, and is the... 
generalized harmonic functions | Arakawa-Kaneko zeta functions | multiple zeta values | modified Bell polynomials | MATHEMATICS | MATHEMATICS, APPLIED | VALUES | POLY-BERNOULLI NUMBERS | Integers | Real numbers | Numbers
Journal Article
International Journal of Number Theory, ISSN 1793-0421, 03/2017, Volume 13, Issue 2, pp. 513 - 528
In this paper, we investigate two kinds of Euler sums that involve the generalized harmonic numbers with arbitrary depth. These sums establish numerous... 
generalized harmonic numbers | Multiple zeta values | Stirling numbers of the first kind | modified Bell polynomials | MATHEMATICS | SERIES | DUALITY | FORMULAS | RIEMANN ZETA
Journal Article
Journal Article
Mathematics (Basel), ISSN 2227-7390, 2019, Volume 7, Issue 3, p. 238
A preferential arrangement on [ [ n ] ] = { 1 , 2 , … , n } is a ranking of the elements of [ [ n ] ] where ties are allowed. The number of preferential... 
MATHEMATICS | Delannoy numbers | VALUES | harmonic algebras | preferential arrangements
Journal Article
Journal of Number Theory, ISSN 0022-314X, 08/2015, Volume 153, pp. 107 - 116
We obtain some formulas for the stuffle product and apply them to derive a decomposition formula for multiple zeta values. Moreover, we give an application to... 
Delannoy number | Multiple zeta value | Stuffle product | MATHEMATICS | DECOMPOSITION
Journal Article
Diamond & Related Materials, ISSN 0925-9635, 2006, Volume 15, Issue 11, pp. 2010 - 2014
Multi-wall carbon nanotube (CNT) films were fabricated by microwave plasma chemical vapor deposition at low temperatures (∼ 500 °C). The films when properly... 
Carbon nanotube | Field emission | Laser irradiation | Post-treatment | laser irradiation | carbon nanotube | post-treatment | field emission | MATERIALS SCIENCE, MULTIDISCIPLINARY | Lasers | Analysis | Nanotechnology | Nanotubes
Journal Article
FILOMAT, ISSN 0354-5180, 2019, Volume 33, Issue 1, pp. 101 - 109
We define the finite Hurwitz-Lerch function H-n((s))(x, y) = Sigma(n-1)(k=0) x(k)/(k+y)(s). Then we explore some properties of them and give some applications,... 
Mellin differential operator | MATHEMATICS, APPLIED | ZETA-FUNCTIONS | SERIES | Hurwitz-Lerch zeta function | Stirling numbers | RIEMANN ZETA | MATHEMATICS | COMBINATORIAL IDENTITIES | modified Bell polynomials | FAMILIES | generalized harmonic function | Finit Hurwitz-Lerch functions | FORMULAS
Journal Article
Journal of Number Theory, ISSN 0022-314X, 2006, Volume 117, Issue 1, pp. 31 - 52
In this paper, we consider two types of extended Euler sums: E p , q ( k ) = ∑ n = 1 ∞ 1 n q ∑ r = 1 kn 1 r p , T p , q ( k ) = ∑ n = 1 ∞ 1 n q ∑ r = 1 ⌊ n / k... 
Zeta function | Euler sum | Bernoulli polynomial | POLYNOMIALS | MATHEMATICS | zeta function | INTEGRAL-REPRESENTATIONS | Computer science
Journal Article
Fibonacci Quarterly, ISSN 0015-0517, 05/2004, Volume 42, Issue 2, pp. 128 - 140
Journal Article
Mediterranean Journal of Mathematics, ISSN 1660-5446, 6/2017, Volume 14, Issue 3, pp. 1 - 13
... with Even Arguments Kwang-Wu Chen and Chan-Liang Chung Abstract. The purpose of this paper is the presentation of an identity which is closely related to the sum relation... 
infinite series and products | alternating multiple zeta values | sum formula | 11M32 | Riemann zeta function | Mathematics, general | multiple zeta value | generating functions | Mathematics | 11M06 | 11B68 | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Journal of Integer Sequences, ISSN 1530-7638, 2003, Volume 6, Issue 4
Journal Article
Journal of Number Theory, ISSN 0022-314X, 01/2016, Volume 158, pp. 33 - 53
Multiple zeta values or r-ford Euler sums are defined byζ(α1,α2,. .,αr)=∑1≤n1 Multiple zeta values | Duality theorems | Secondary | Sum formulas | Primary | MATHEMATICS
Journal Article
Journal of Integer Sequences, ISSN 1530-7638, 2001, Volume 4, Issue 1
Journal Article
Journal of Integer Sequences, 2011, Volume 14, Issue 4, pp. 1 - 8
Journal Article
Journal of Number Theory, ISSN 0022-314X, 2007, Volume 124, Issue 1, pp. 142 - 150
A sequence b n is the binomial transform of the sequence a n if b n = ∑ k = 0 n ( n k ) a k . We derive a general identity for such pairs of sequences. Various... 
Bernoulli numbers | Generalized Seidel matrix | Binomial transform | MATHEMATICS | generalized seidel matrix | binomial transform | EULER | RECURRENCE FORMULA
Journal Article
Pacific Journal of Mathematics, ISSN 0030-8730, 2003, Volume 208, Issue 1, pp. 39 - 52
In this paper, we investigate the zeta function [GRAPHICS] . P (n(1) + a(1) ,..., n(r) + a(r))(-s), where a(i) greater than or equal to 0, chi(i) is a... 
MATHEMATICS | NUMBERS
Journal Article
12/2018
We express some general type of infinite series such as $$ \sum^\infty_{n=1}\frac{F(H_n^{(m)}(z),H_n^{(2m)}(z),\ldots,H_n^{(\ell m)}(z))}... 
Mathematics - Number Theory
Journal Article
07/2017
Let $p,x$ be real numbers, and $s$ be a complex number, with $\Re(s)>1-r$, $p\geq 1$, and $x+1>0$. The zeta function $Z^{\bf\alpha}_p(s;x)$ is defined by $$... 
Mathematics - Number Theory
Journal Article
08/2013
A semiconductor device and a method for fabricating a semiconductor device is disclosed. An exemplary semiconductor device includes a semiconductor substrate... 
SEMICONDUCTOR DEVICES | BASIC ELECTRIC ELEMENTS | ELECTRIC SOLID STATE DEVICES NOT OTHERWISE PROVIDED FOR | ELECTRICITY
Patent
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