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mathematics (19) 19
mathematics, general (7) 7
mathematics, applied (6) 6
secondary 40a25 (6) 6
harmonic numbers (5) 5
primary: 05a19 (5) 5
secondary: 40a25 (5) 5
derivative operator (4) 4
number theory (4) 4
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harmonics (3) 3
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transforms (3) 3
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abel’s lemma on summation by parts (2) 2
algebra (2) 2
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binomials (2) 2
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identities (2) 2
mathematical analysis (2) 2
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theorems (2) 2
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41a36 (1) 1
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abel's transformation (1) 1
abel’s transformation (1) 1
algebra of matrices (1) 1
ams classification: primary, 65b10, secondary, 40a25, secondary, 65e05 (1) 1
ams subject classification: primary 40a25, 65d30 (1) 1
analysis (1) 1
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asymptotic expansion (1) 1
banach algebra (1) 1
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binet formula (1) 1
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chu-vandermonde convolution (1) 1
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Journal of Information and Optimization Sciences, ISSN 0252-2667, 10/2018, Volume 39, Issue 7, pp. 1483 - 1504
This study is devoted to the polynomial representation of the matrix pth root functions. The Fibonacci-Hörner decomposition of the matrix powers and some... 
Primary 15A99 | Secondary 40A25 | Fibonacci-Hörner decomposition | Binet formula | Principal matrix pth root
Journal Article
Integral Transforms and Special Functions, ISSN 1065-2469, 10/2017, Volume 28, Issue 10, pp. 703 - 709
In terms of the telescoping method, a new binomial identity is established. By applying the derivative operators, we derive several interesting harmonic number... 
Secondary: 40A25 | derivative operator | Telescoping method | harmonic number identity | Primary: 05A19 | MATHEMATICS | MATHEMATICS, APPLIED | SUMS | Operators (mathematics) | Telescoping
Journal Article
The Ramanujan Journal, ISSN 1382-4090, 10/2015, Volume 38, Issue 1, pp. 123 - 128
... constant · Asymptotic expansion Mathematics Subject Classi cation Primary 41A60 · 40A25 1 Introduction Ramanujan (see [ 1 , p. 531] and [ 6 , p. 276]) proposed... 
Euler–Mascheroni constant | Fourier Analysis | Asymptotic expansion | Functions of a Complex Variable | Primary 41A60 | Harmonic numbers | Field Theory and Polynomials | Mathematics | Number Theory | 40A25 | Combinatorics | MATHEMATICS | Euler-Mascheroni constant
Journal Article
The American Mathematical Monthly, ISSN 0002-9890, 05/2019, Volume 126, Issue 5, pp. 448 - 448
Journal Article
Integral Transforms and Special Functions, ISSN 1065-2469, 04/2013, Volume 24, Issue 4, pp. 324 - 330
By applying the derivative operators to Chu-Vandermonde convolution, several general harmonic number identities are established. 
Secondary: 40A25 | derivative operator | harmonic number identity | Primary: 05A19 | Chu-Vandermonde convolution | Harmonics | Operators | Convolution | Derivatives | Integrals | Transforms
Journal Article
The Ramanujan Journal, ISSN 1382-4090, 1/2018, Volume 45, Issue 1, pp. 73 - 94
... Subject Classification Primary 05A19 · Secondary 40A25 1 Introduction A harmonic number is a number of the form H n = n null k=1 1 k The rst author is supported... 
Fourier Analysis | Secondary 40A25 | Functions of a Complex Variable | Difference operator | Harmonic numbers | Field Theory and Polynomials | Primary 05A19 | Abel’s transformation | Mathematics | Number Theory | Combinatorics | MATHEMATICS | IDENTITIES | Abel's transformation | SUMS
Journal Article
Results in Mathematics, ISSN 1422-6383, 6/2012, Volume 61, Issue 3, pp. 209 - 221
... identities, which involve the classical harmonic numbers and their variants. Mathematics Subject Classification (2000). Primary 05A19; Secondary 40A25. Keywords. Harmonic... 
telescoping method | Secondary 40A25 | Catalan constant | Harmonic numbers | Primary 05A19 | Mathematics, general | Abel’s lemma on summation by parts | partial fraction decomposition | Mathematics | Abel's lemma on summation by parts | MATHEMATICS | MATHEMATICS, APPLIED | Statistics | Telescope
Journal Article
The American Mathematical Monthly, ISSN 0002-9890, 07/2018, Volume 125, Issue 6, pp. 554 - 557
We show how to modify the last term of the partial sum of an alternating series so as to get an upper bound on the limit better than the standard one obtained... 
Primary 40A25 | MATHEMATICS
Journal Article
The American mathematical monthly, ISSN 1930-0972, 2018, Volume 125, Issue 3, pp. 245 - 256
We present an easily defined countable family of permutations of the natural numbers for which explicit rearrangements (i.e., the sums induced by the... 
Primary 40A25 | MATHEMATICS
Journal Article
The American Mathematical Monthly, ISSN 0002-9890, 04/2018, Volume 125, Issue 4, pp. 360 - 364
We present a new proof of Johnsonbaugh's estimates for the error in an alternating series based on an idea of R. M. Young. We also use this same idea to prove... 
Primary 40A05 | Secondary 40A25 | MATHEMATICS
Journal Article
Mediterranean Journal of Mathematics, ISSN 1660-5446, 10/2018, Volume 15, Issue 5, pp. 1 - 12
...), and then generalise to the case of a norm-unital Banach algebra (Sect. 4). Mathematics Subject Classification. Primary: 40A25, 41A99, 46H99; Secondary: 26D99, 47A50, 65D20... 
Estimate | Mathematics | Hermitian element | Exponential function | 47A50 | Spectrum | 41A99 | 46H99 | 65D20 | Secondary: 26D99 | Banach algebra | Inequalities | Primary: 40A25 | Mathematics, general | Norm | Asymptotic approximation | Distance
Journal Article
Archiv der Mathematik, ISSN 0003-889X, 07/2009, Volume 93, Issue 1, pp. 37 - 45
We prove in this paper that for every x >= 0, root 2 pi e . e(-omega) (x + omega/e) (x + 1/2) < Gamma (x + 1) <= alpha . root 2 pi e . e(-omega) (x + omega/e)... 
Secondary 26D07 | Mathematics Subject Classification : Primary: 40A25 | MATHEMATICS | Factorial function | Digamma function | Stirling's formula | Gamma function | Numeric series | Burnside's formula and inequalities
Journal Article
Integral Transforms and Special Functions, ISSN 1065-2469, 03/2014, Volume 25, Issue 3, pp. 203 - 214
In terms of the telescoping method, a simple binomial sum is given. By applying the derivative operators to the equation just mentioned, we establish several... 
Secondary: 40A25 | telescoping method | derivative operator | harmonic number identity | Primary: 05A19 | MATHEMATICS | MATHEMATICS, APPLIED | Binomials
Journal Article
Results in Mathematics, ISSN 1422-6383, 3/2018, Volume 73, Issue 1, pp. 1 - 14
...) are established as consequences. Mathematics Subject Classification. Primary 05A19; Secondary 40A25. Keywords. Abel’s lemma on summation by parts, harmonic numbers... 
Secondary 40A25 | generalized harmonic numbers | Primary 05A19 | Mathematics, general | Abel’s lemma on summation by parts | partial fraction decomposition | Mathematics | harmonic numbers | MATHEMATICS | MATHEMATICS, APPLIED | IDENTITIES | Abel's lemma on summation by parts | SUMMATION
Journal Article
Integral Transforms and Special Functions, ISSN 1065-2469, 09/2015, Volume 26, Issue 9, pp. 667 - 677
In terms of the derivative operator and a binomial sum from the telescoping method, we establish a family of summation formulae involving harmonic numbers.... 
Secondary: 40A25 | telescoping method | harmonic numbers | derivative operator | Primary: 05A19 | MATHEMATICS | MATHEMATICS, APPLIED | Harmonics | Telescoping | Operators | Integrals | Transforms | Derivatives | Binomials
Journal Article
Integral Transforms and Special Functions, ISSN 1065-2469, 12/2015, Volume 26, Issue 12, pp. 971 - 984
By means of the partial fraction decomposition method, we establish some summations of generalized q-harmonic numbers with finite series. We further explore... 
Secondary: 40A25 | partial fraction decomposition method | summation identities | generalized q-harmonic number | Primary: 05A19 | MATHEMATICS | MATHEMATICS, APPLIED | Harmonics | Integrals | Lists | Mathematical analysis | Transforms | Series (mathematics) | Decomposition
Journal Article
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, ISSN 0025-5858, 4/2015, Volume 85, Issue 1, pp. 23 - 41
For positives integers $$\alpha _{1}, \alpha _{2}, \ldots , \alpha _{r}$$ α 1 , α 2 , … , α r with $$\alpha _{r} \ge 2$$ α r ≥ 2 , the multiple zeta value or... 
33E99 | Weighted sum formula | Multiple zeta values | Mathematics | Topology | Geometry | Algebra | Secondary 11M99 | 40B05 | Mathematics, general | Number Theory | Differential Geometry | Drinfeld integral | Shuffle product | Primary 40A25 | MATHEMATICS
Journal Article
Archiv der Mathematik, ISSN 0003-889X, 10/2008, Volume 91, Issue 4, pp. 330 - 338
For positive integers $$\alpha_{1}, \alpha_{2}, \ldots ,\alpha_{r}$$ with a r  = 2, the multiple zeta value or r-fold Euler sum is defined as [2] $$ \varsigma... 
sum formula | Secondary 11M99, 33E99 | multiple zeta values | Euler sums | Mathematics, general | Primary 40A25, 40B05 | Mathematics | Drinfeld integral | Multiple zeta values | Sum formula | MATHEMATICS
Journal Article
Journal of Difference Equations and Applications, ISSN 1023-6198, 12/2008, Volume 14, Issue 12, pp. 1279 - 1287
We consider the number π coth π which is transcendental in view of algebraic independence of π and e π (due to Nesterenko's work in 1996). Studying certain... 
Secondary 33C20, 40A25 | rational function | hypergeometric series | Zeilberger's algorithm | Primary 11J70, 11B37, 39A05 | Continued fraction | Hypergeometric series | Rational function
Journal Article
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