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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
In this paper, we provide a recurrence relation for determining the coefficients of Ramanujan’s asymptotic expansion for the $$n$$ n th harmonic number. 
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
Resultate der Mathematik, ISSN 1420-9012, 2018, Volume 74, Issue 1, pp. 1 - 20
In this paper, we obtain some new exponential-function approximations and inequalities of the Somos’ quadratic recurrence constant, using its relation with the... 
40A20 | 65B10 | Somos’ quadratic recurrence constant | inequalities | 65B15 | Mathematics, general | 40A05 | Mathematics | exponential function | 40A25 | generalized Euler’s constant | MATHEMATICS | MATHEMATICS, APPLIED | CONTINUED-FRACTION APPROXIMATION | GAMMA FUNCTION | generalized Euler's constant | Somos' quadratic recurrence constant
Journal Article
Analysis, ISSN 0174-4747, 11/2016, Volume 36, Issue 4, pp. 223 - 230
We introduce a sequence of real functions which converges to the constant function where γ is the Euler–Mascheroni constant. We determine a point where the... 
Euler–Mascheroni constant | 33B15 | rate of convergence | digamma function | 11Y60 | harmonic number | 40A25 | Euler-Mascheroni constant
Journal Article
Bollettino dell'Unione Matematica Italiana, ISSN 1972-6724, 12/2018, Volume 11, Issue 4, pp. 541 - 555
Consider a sequence $$(a_n)_{n\ge 1}$$ (an)n≥1 of complex numbers such that for some positive number p we have $$\lim _{n\rightarrow \infty... 
Riemann integrable functions | 26A42 | Stolz-Cesàro lemma | Mathematics, general | Convergence in the mean | Euler’s totient function | 40A05 | Mathematics | The law of large numbers | 40A25 | Continuous functions
Journal Article
Mediterranean Journal of Mathematics, ISSN 1660-5446, 6/2016, Volume 13, Issue 3, pp. 929 - 938
Let $${\pi(x)}$$ π ( x ) be the number of primes not exceeding x. We produce new explicit bounds for $${\pi(x)}$$ π ( x ) and we use them to obtain a fine... 
prime numbers | 11A41 | Explicit estimates | Mathematics, general | 11Y60 | Mathematics | 40A25 | 26D15 | MATHEMATICS | MATHEMATICS, APPLIED | ADDITIVE-FUNCTIONS | SUMS | Number Theory
Journal Article
Integral Transforms and Special Functions, ISSN 1065-2469, 04/2013, Volume 24, Issue 4, pp. 324 - 330
By applying the derivative operators to Chu-Vandermonde convolution, several general harmonic number identities are established. 
Secondary: 40A25 | derivative operator | harmonic number identity | Primary: 05A19 | Chu-Vandermonde convolution | Harmonics | Operators | Convolution | Derivatives | Integrals | Transforms
Journal Article
Numerical Algorithms, ISSN 1017-1398, 3/2017, Volume 74, Issue 3, pp. 937 - 949
Let {x m } be a vector sequence that satisfies x m ∼ s + ∑ i = 1 ∞ α i g i ( m ) as m → ∞ , $$\boldsymbol{x}_{m}\sim... 
Numeric Computing | Vector extrapolation methods | Theory of Computation | 65B10 | Algorithms | Algebra | Numerical Analysis | Acceleration of convergence | Computer Science | Vectorized generalized Richardson extrapolation process | 40A05 | 65B05 | 40A25 | MATHEMATICS, APPLIED
Journal Article
The Ramanujan Journal, ISSN 1382-4090, 1/2018, Volume 45, Issue 1, pp. 73 - 94
In terms of Abel’s transformation on difference operators, we establish four families of summation formulas involving generalized harmonic numbers. They... 
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
The Ramanujan Journal, ISSN 1382-4090, 4/2012, Volume 27, Issue 3, pp. 343 - 347
We give a natural derivation of a formula of Ramanujan, described by B.C. Berndt as “enigmatic”, for the harmonic series. 
Ramanujan | 33E99 | Functions of a Complex Variable | Field Theory and Polynomials | Harmonic series | 33-01 | Mathematics | 33F05 | 65D20 | Fourier Analysis | Number Theory | 40A25 | Combinatorics | Enigmatic formula | MATHEMATICS
Journal Article
Constructive Approximation, ISSN 0176-4276, 12/2012, Volume 36, Issue 3, pp. 331 - 352
Journal Article
Functiones et Approximatio, Commentarii Mathematici, ISSN 0208-6573, 2012, Volume 46, Issue 1, pp. 63 - 77
For positive integers \alpha_{1}, \alpha_{2}, \ldots, \alpha_{r} with \alpha_{r} \geq 2, the multiple zeta value or r-fold Euler sum is defined by... 
Euler sums | Stuffle formulae | Multiple zeta value | Hurwitz zeta function | 33E99 | 11M99 | stuffle formulae | 40B05 | multiple zeta value | 40A25
Journal Article
Results in Mathematics, ISSN 1422-6383, 6/2012, Volume 61, Issue 3, pp. 209 - 221
By means of Abel’s lemma on summation by parts, we derive several infinite series identities, which involve the classical harmonic numbers and their variants. 
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
Bulletin of the Belgian Mathematical Society - Simon Stevin, ISSN 1370-1444, 10/2010, Volume 17, Issue 4, pp. 741 - 747
For the generalized-Euler-constant function a bar right arrow gamma(a) := lim(n ->infinity) (Sigma(n-1)(i=0)1/a+i - ln a+n-1/a) defined on R+, the expansion... 
Generalized-Euler-constant function | Estimate | Hurwitz-zeta function | MATHEMATICS | estimate | generalized-Euler-constant function | Mathematical constants | Functions | Research | Functional equations | 11Y60 | 40A05 | 40A25
Journal Article
The Ramanujan Journal, ISSN 1382-4090, 2/2010, Volume 21, Issue 2, pp. 123 - 143
We introduce a natural definition for sums of the form $$\sum_{\nu=1}^xf(\nu)$$ when the number of terms x is a rather arbitrary real or even complex number.... 
33B99 | Functions of a Complex Variable | Field Theory and Polynomials | Mathematics | Interpolation | Summation identities | Fourier Analysis | 40C99 | Fractional sum | Number Theory | 40A25 | Combinatorics | Summation | 41A05 | MATHEMATICS
Journal Article
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