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

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

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

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

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

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

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

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

Secondary: 40A25 | derivative operator | harmonic number identity | Primary: 05A19 | Chu-Vandermonde convolution | Harmonics | Operators | Convolution | Derivatives | Integrals | Transforms

Journal Article

10.
Full Text
Chlodowsky type generalization of (p, q)-Szász operators involving Brenke type polynomials

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, ISSN 1578-7303, 10/2018, Volume 112, Issue 4, pp. 1443 - 1462

In this paper, we introduce a Chlodowsky variant of the Szász operators by means of the (p, q)-integers as well as of the (p, q)-Gaussian binomial...

Secondary 40A25 | Theoretical, Mathematical and Computational Physics | Weighted approximation | (p, q)$$ ( p , q ) -Szász type operators involving Brenke type polynomials | Mathematics | Primary 41A10 | 41A25 | 41A36 | 11B83 | Korovkin and Voronovskaja type approximation theorems | Mathematics, general | Applications of Mathematics | Rate of convergence | (p, q) -Szász type operators involving Brenke type polynomials | MATHEMATICS | (p, q)-Szasz type operators involving Brenke type polynomials | APPROXIMATION THEOREMS | STATISTICAL CONVERGENCE | Q)-INTEGERS | VARIANT

Secondary 40A25 | Theoretical, Mathematical and Computational Physics | Weighted approximation | (p, q)$$ ( p , q ) -Szász type operators involving Brenke type polynomials | Mathematics | Primary 41A10 | 41A25 | 41A36 | 11B83 | Korovkin and Voronovskaja type approximation theorems | Mathematics, general | Applications of Mathematics | Rate of convergence | (p, q) -Szász type operators involving Brenke type polynomials | MATHEMATICS | (p, q)-Szasz type operators involving Brenke type polynomials | APPROXIMATION THEOREMS | STATISTICAL CONVERGENCE | Q)-INTEGERS | VARIANT

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

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

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

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

In this paper, we provide the Euler–Maclaurin expansions for (offset) trapezoidal rule approximations of the finite-range integrals $I[f]=\int^{b}_{a}f(x)\,dx$...

Asymptotic expansions | Trapezoidal rule | 30E15 | Mathematics | 41A60 | 65D30 | Euler–Maclaurin expansions | Endpoint singularities | Stieltjes constants | 65B15 | Numerical Analysis | Analysis | Hadamard finite part | Zeta function | Algebraic singularities | 40A25 | Logarithmic singularities | Euler-Maclaurin expansions | EXTENSION | MATHEMATICS | PERIODIZING VARIABLE TRANSFORMATIONS | NUMERICAL-INTEGRATION | Computer science

Asymptotic expansions | Trapezoidal rule | 30E15 | Mathematics | 41A60 | 65D30 | Euler–Maclaurin expansions | Endpoint singularities | Stieltjes constants | 65B15 | Numerical Analysis | Analysis | Hadamard finite part | Zeta function | Algebraic singularities | 40A25 | Logarithmic singularities | Euler-Maclaurin expansions | EXTENSION | MATHEMATICS | PERIODIZING VARIABLE TRANSFORMATIONS | NUMERICAL-INTEGRATION | Computer science

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

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

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

Primary 40A25 | MATHEMATICS

Journal Article

Journal of Mathematical Biology, ISSN 0303-6812, 11/2010, Volume 61, Issue 5, pp. 695 - 714

The structured coalescent describes the ancestral relationship among sampled genes from a geographically structured population. The aim of this article is to...

Central limit theorem | Mathematics | Mathematical Biology in General | Applications of Mathematics | Conservative and nonconservative migration | 40A25 | Structured coalescent process | Coalescence times | GENES | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | GENEALOGICAL PROCESS | POPULATION-SIZE | Genetics, Population | Markov Chains | Phylogeography | Genes - genetics | Mutation - genetics | Haploidy | Algorithms | Animals | Time Factors | Population Density | Animal Migration | Models, Genetic | Population Dynamics | Genetics | Models | Research | Cell migration | Limit theorems (Probability theory)

Central limit theorem | Mathematics | Mathematical Biology in General | Applications of Mathematics | Conservative and nonconservative migration | 40A25 | Structured coalescent process | Coalescence times | GENES | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | GENEALOGICAL PROCESS | POPULATION-SIZE | Genetics, Population | Markov Chains | Phylogeography | Genes - genetics | Mutation - genetics | Haploidy | Algorithms | Animals | Time Factors | Population Density | Animal Migration | Models, Genetic | Population Dynamics | Genetics | Models | Research | Cell migration | Limit theorems (Probability theory)

Journal Article

19.
Full Text
An interplay between a generalized-Euler-constant function and the Hurwitz zeta function

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

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

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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