The American Mathematical Monthly, ISSN 0002-9890, 02/2020, Volume 127, Issue 2, pp. 174 - 174

Journal Article

Aequationes mathematicae, ISSN 0001-9054, 2/2019, Volume 93, Issue 1, pp. 299 - 309

Roger Cuculière [Problem 11998, The American Mathematical Monthly 124 no. 7 (2017)] has posed the following problem: Find all continuous functions $$f: \mathbb...

Alternative (conditional) functional equations | D’Alembert’s equation | Primary 39B52 | Analysis | Mathematics | Combinatorics | Fubini’s Theorem | Secondary 26A09 | Invariant ideals | Continuity (mathematics)

Alternative (conditional) functional equations | D’Alembert’s equation | Primary 39B52 | Analysis | Mathematics | Combinatorics | Fubini’s Theorem | Secondary 26A09 | Invariant ideals | Continuity (mathematics)

Journal Article

Results in Mathematics, ISSN 1422-6383, 6/2018, Volume 73, Issue 2, pp. 1 - 13

This paper presents an interpolation-based method for bounding some smooth functions, including the arctangent functions related to Shafer’s inequality. Given...

Shafer’s inequality | Secondary 26D99 | Primary 26A09 | arctangent function | approximations and estimations | definite integral | 42A10 | Mathematics, general | Mathematics | bounded bounds

Shafer’s inequality | Secondary 26D99 | Primary 26A09 | arctangent function | approximations and estimations | definite integral | 42A10 | Mathematics, general | Mathematics | bounded bounds

Journal Article

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, ISSN 1578-7303, 1/2019, Volume 113, Issue 1, pp. 1 - 9

In the paper, the authors discuss the Bell polynomials and a sequence of polynomials applied to the theory of differential equations. Concretely speaking, the...

Faà di Bruno formula | 11C08 | Generating function | Secondary 11B73 | Differential equation | Theoretical, Mathematical and Computational Physics | 33B10 | Mathematics | Bell polynomial | Explicit formula | Primary 11B83 | Derivative | Mathematics, general | 26A06 | Applications of Mathematics | Identity | 26A09 | Stirling number | INEQUALITIES | Faa di Bruno formula | TERMS | DIAGONAL RECURRENCE RELATIONS | STIRLING NUMBERS | MATHEMATICS | 2ND KIND | Functions (mathematics) | Polynomials | Mathematical analysis | Combinatorial analysis | Differential equations | Identities

Faà di Bruno formula | 11C08 | Generating function | Secondary 11B73 | Differential equation | Theoretical, Mathematical and Computational Physics | 33B10 | Mathematics | Bell polynomial | Explicit formula | Primary 11B83 | Derivative | Mathematics, general | 26A06 | Applications of Mathematics | Identity | 26A09 | Stirling number | INEQUALITIES | Faa di Bruno formula | TERMS | DIAGONAL RECURRENCE RELATIONS | STIRLING NUMBERS | MATHEMATICS | 2ND KIND | Functions (mathematics) | Polynomials | Mathematical analysis | Combinatorial analysis | Differential equations | Identities

Journal Article

Journal of Number Theory, ISSN 0022-314X, 02/2016, Volume 159, pp. 89 - 100

In the paper, the authors find two closed forms involving the Stirling numbers of the second kind and in terms of a determinant of combinatorial numbers for...

Bernoulli number | Bernoulli polynomial | Stirling numbers of the second kind | Determinant | Closed form | FUNCTION (B(X)-A(X))/X | MATHEMATICS | INEQUALITIES | IDENTITIES | EXPLICIT FORMULAS | STIRLING NUMBERS

Bernoulli number | Bernoulli polynomial | Stirling numbers of the second kind | Determinant | Closed form | FUNCTION (B(X)-A(X))/X | MATHEMATICS | INEQUALITIES | IDENTITIES | EXPLICIT FORMULAS | STIRLING NUMBERS

Journal Article

Milan Journal of Mathematics, ISSN 1424-9286, 12/2016, Volume 84, Issue 2, pp. 217 - 230

A simple addition to the collection of superoscillatory functions is constructed, in the form of a square-integrable sinc function which is band-limited yet in...

Fourier | band-limited | Analysis | asymptotics | Mathematics, general | superoscillatory | Mathematics | 41A60 | 26A09 | 42A38 | 62E17 | SUPERRESOLUTION | MATHEMATICS | MATHEMATICS, APPLIED | EVANESCENT

Fourier | band-limited | Analysis | asymptotics | Mathematics, general | superoscillatory | Mathematics | 41A60 | 26A09 | 42A38 | 62E17 | SUPERRESOLUTION | MATHEMATICS | MATHEMATICS, APPLIED | EVANESCENT

Journal Article

Results in Mathematics, ISSN 1422-6383, 3/2018, Volume 73, Issue 1, pp. 1 - 8

In this paper, we present a continued fraction approximation for the gamma function. This approximation is fast in comparison with the recently discovered...

33B15 | inequality | 26D20 | gamma function | multiple-correction method | Mathematics, general | Mathematics | numerical computations | 26A09 | Continued fraction | MATHEMATICS | MATHEMATICS, APPLIED | MULTIPLE-CORRECTION | Analysis | Equality

33B15 | inequality | 26D20 | gamma function | multiple-correction method | Mathematics, general | Mathematics | numerical computations | 26A09 | Continued fraction | MATHEMATICS | MATHEMATICS, APPLIED | MULTIPLE-CORRECTION | Analysis | Equality

Journal Article

Acta Universitatis Sapientiae, Mathematica, ISSN 1844-6094, 12/2017, Volume 9, Issue 2, pp. 348 - 359

In the paper, the authors derive an explicit formula for derivative polynomials of the tangent function, deduce an explicit formula for tangent numbers, pose...

open problem | 16A24 | explicit formula | tangent number | derivative polynomial | 26C99 | 33B10 | 26A06 | tangent function | 26A09 | 42A05 | Tangent function | Open problem | Tangent number | Derivative polynomial | Explicit formula

open problem | 16A24 | explicit formula | tangent number | derivative polynomial | 26C99 | 33B10 | 26A06 | tangent function | 26A09 | 42A05 | Tangent function | Open problem | Tangent number | Derivative polynomial | Explicit formula

Journal Article

Journal of Difference Equations and Applications, ISSN 1023-6198, 02/2016, Volume 22, Issue 2, pp. 177 - 187

If the difference of two real homographic functions is nonnegative, then it is constant. Motivated by this property, we determine all pairs of subcommuting...

39B12 | homographic function | iteration group | commuting functions | 26A09 | 26D07 | 26A18 | 39B72 | subcommuting functions | supercommuting functions | MATHEMATICS, APPLIED | Applied mathematics | Differential equations | Difference equations | Constants | Transforms

39B12 | homographic function | iteration group | commuting functions | 26A09 | 26D07 | 26A18 | 39B72 | subcommuting functions | supercommuting functions | MATHEMATICS, APPLIED | Applied mathematics | Differential equations | Difference equations | Constants | Transforms

Journal Article

Symmetry, ISSN 2073-8994, 06/2019, Volume 11, Issue 6, p. 782

In this paper, the authors present a closed formula for the Horadam polynomials in terms of a tridiagonal determinant and, as applications of the...

Horadam polynomial | Pell-Lucas polynomial | Generalized Fibonacci polynomial | Chebyshev polynomial of the first kind | Tridiagonal determinant | Closed formula | Lucas polynomial | Chebyshev polynomial of the second kind | 11B39 | MATRIX | tridiagonal determinant | NUMBERS | MULTIDISCIPLINARY SCIENCES | 11C20 | REPRESENTATION | generalized Fibonacci polynomial | EXPRESSIONS | 11Y55 | 11B83 | RECURRENCE RELATION | 26A06 | FIBONACCI | closed formula | 26A09 | 26C05 | Horadam polynomial, tridiagonal determinant | Pell–Lucas polynomial

Horadam polynomial | Pell-Lucas polynomial | Generalized Fibonacci polynomial | Chebyshev polynomial of the first kind | Tridiagonal determinant | Closed formula | Lucas polynomial | Chebyshev polynomial of the second kind | 11B39 | MATRIX | tridiagonal determinant | NUMBERS | MULTIDISCIPLINARY SCIENCES | 11C20 | REPRESENTATION | generalized Fibonacci polynomial | EXPRESSIONS | 11Y55 | 11B83 | RECURRENCE RELATION | 26A06 | FIBONACCI | closed formula | 26A09 | 26C05 | Horadam polynomial, tridiagonal determinant | Pell–Lucas polynomial

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 10/2014, Volume 418, Issue 1, pp. 185 - 210

A modification of the Taylor expansion for the complex exponential function eix, x∈R, is proposed yielding precise moment-type estimates of the accuracy of the...

Characteristic function | Taylor series | Fourier transform | Accuracy of approximation | Moment inequality | MATHEMATICS, APPLIED | ABSOLUTE CONSTANT | POISSON RANDOM SUMS | DISTRIBUTIONS | REFINEMENT | MATHEMATICS | LYAPUNOV THEOREM | UPPER-BOUNDS | BERRY-ESSEEN INEQUALITY | IMPROVEMENT | CONVERGENCE RATE | CENTRAL-LIMIT-THEOREM

Characteristic function | Taylor series | Fourier transform | Accuracy of approximation | Moment inequality | MATHEMATICS, APPLIED | ABSOLUTE CONSTANT | POISSON RANDOM SUMS | DISTRIBUTIONS | REFINEMENT | MATHEMATICS | LYAPUNOV THEOREM | UPPER-BOUNDS | BERRY-ESSEEN INEQUALITY | IMPROVEMENT | CONVERGENCE RATE | CENTRAL-LIMIT-THEOREM

Journal Article

SpringerPlus, ISSN 2193-1801, 12/2016, Volume 5, Issue 1, pp. 1 - 9

In this paper we construct some real algebras by using elementary functions, and discuss some relations between several axioms and its related conditions for...

Trace | BCK -algebra | d -algebra | Science, Humanities and Social Sciences, multidisciplinary | Analytic real algebra | 26A09 | 06F35 | d-algebra | BCK-algebra | MULTIDISCIPLINARY SCIENCES

Trace | BCK -algebra | d -algebra | Science, Humanities and Social Sciences, multidisciplinary | Analytic real algebra | 26A09 | 06F35 | d-algebra | BCK-algebra | MULTIDISCIPLINARY SCIENCES

Journal Article

Tokyo Journal of Mathematics, ISSN 0387-3870, 2017, Volume 34, Issue 2, pp. 345 - 352

We consider real-valued twice differentiable functions defined on an open interval. Our main result states that if a function f satisfies some inequalities...

Functional-differential inequality | Convex mappings | Exponential mapping | HYERS-ULAM STABILITY | MATHEMATICS | convex mappings | exponential mapping | CONSTANT-COEFFICIENTS | functional-differential inequality | EQUATIONS | 1ST-ORDER | OPERATORS | 34K38 | 39B62 | 26A51 | 34A40 | 26A09 | 26D10

Functional-differential inequality | Convex mappings | Exponential mapping | HYERS-ULAM STABILITY | MATHEMATICS | convex mappings | exponential mapping | CONSTANT-COEFFICIENTS | functional-differential inequality | EQUATIONS | 1ST-ORDER | OPERATORS | 34K38 | 39B62 | 26A51 | 34A40 | 26A09 | 26D10

Journal Article

Numerical Algorithms, ISSN 1017-1398, 7/2015, Volume 69, Issue 3, pp. 595 - 610

The main object of this paper is to propose a product approximation for the gamma function. The estimates derived here are studied via the theory of completely...

33B15 | Haussdorff-Bernstein-Widder theorem | Factorial function | Numerical computations | Numeric Computing | Speed of convergence | Stirling’s formula | Theory of Computation | Gamma function | Two-sided inequalities | Complete monotonicity | Algorithms | Algebra | Asymptotic series | Primary 26A09 | Product approximations | Secondary 26D20 | Numerical Analysis | Computer Science | MATHEMATICS, APPLIED | Stirling's formula

33B15 | Haussdorff-Bernstein-Widder theorem | Factorial function | Numerical computations | Numeric Computing | Speed of convergence | Stirling’s formula | Theory of Computation | Gamma function | Two-sided inequalities | Complete monotonicity | Algorithms | Algebra | Asymptotic series | Primary 26A09 | Product approximations | Secondary 26D20 | Numerical Analysis | Computer Science | MATHEMATICS, APPLIED | Stirling's formula

Journal Article

Real Analysis Exchange, ISSN 0147-1937, 1/2015, Volume 40, Issue 1, pp. 219 - 226

This article discusses the definitions and properties of exponential and logarithmic functions. The treatment is based on the basic properties of real numbers,...

Mathematical differentiation | Definite integrals | Logarithmic functions | Rational numbers | Inroads | Exponential functions | Mathematical functions | 26A06 | Exponential Functions | Logarithmic Functions | Differentiation | 26A09 | 26A24

Mathematical differentiation | Definite integrals | Logarithmic functions | Rational numbers | Inroads | Exponential functions | Mathematical functions | 26A06 | Exponential Functions | Logarithmic Functions | Differentiation | 26A09 | 26A24

Journal Article

International Journal of Dynamics and Control, ISSN 2195-268X, 9/2014, Volume 2, Issue 3, pp. 247 - 253

In this paper, we examine an exponential stability result in $$L^2-$$ L 2 - norm of the classical solution of shallow water equations. By using Riemann...

Shallow water equations | Engineering | Vibration, Dynamical Systems, Control | 76B75 | Control | 35L50 | 93D15 | Lyapunov stability | Feedback control | 26A09 | Riemann invariants | Complexity

Shallow water equations | Engineering | Vibration, Dynamical Systems, Control | 76B75 | Control | 35L50 | 93D15 | Lyapunov stability | Feedback control | 26A09 | Riemann invariants | Complexity

Journal Article

Analysis, ISSN 0174-4747, 02/2016, Volume 36, Issue 1, pp. 39 - 48

Two differential transforms involving the Gauss hypergeometric function in the kernels are considered. They generalize the classical Riemann–Liouville and...

Fractional differential transforms | 33C10 | 26A33 | 33C20 | generalized hypergeometric series | generalized Lauricella series in several variables | gamma Bessel density | 33C50 | Bessel functions of the first kind | 33C60 | 26A09

Fractional differential transforms | 33C10 | 26A33 | 33C20 | generalized hypergeometric series | generalized Lauricella series in several variables | gamma Bessel density | 33C50 | Bessel functions of the first kind | 33C60 | 26A09

Journal Article

Integral Transforms and Special Functions, ISSN 1065-2469, 12/2008, Volume 19, Issue 12, pp. 869 - 883

Two integral transforms involving the Gauss-hypergeometric function in the kernels are considered. They generalize the classical Riemann-Liouville and...

33C10 | 26A33 | 33C20 | fractional integral transforms | generalized hypergeometric series | Bessel function of the first kind | 33C60 | 26A09 | cosine and sine trigonometric functions | 33C05 | generalized Wright function | Cosine and sine trigonometric functions | Generalized hypergeometric series | Generalized Wright function | Fractional integral transforms | MATHEMATICS | MATHEMATICS, APPLIED

33C10 | 26A33 | 33C20 | fractional integral transforms | generalized hypergeometric series | Bessel function of the first kind | 33C60 | 26A09 | cosine and sine trigonometric functions | 33C05 | generalized Wright function | Cosine and sine trigonometric functions | Generalized hypergeometric series | Generalized Wright function | Fractional integral transforms | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, ISSN 1578-7303, 9/2014, Volume 108, Issue 2, pp. 827 - 832

For certain pairs of real functions $$f$$ f and $$g$$ g defined and bounded in a compact interval $$[a,b]$$ [ a , b ] , we give a simple characteristic...

26A42 | Real function | Theoretical, Mathematical and Computational Physics | Riemann-Stieltjes integral | Mathematics, general | Mathematics | Applications of Mathematics | 26A09 | Bounded function | MATHEMATICS | Intervals | Integrals | Texts

26A42 | Real function | Theoretical, Mathematical and Computational Physics | Riemann-Stieltjes integral | Mathematics, general | Mathematics | Applications of Mathematics | 26A09 | Bounded function | MATHEMATICS | Intervals | Integrals | Texts

Journal Article

Mathematische Nachrichten, ISSN 0025-584X, 03/2012, Volume 285, Issue 4, pp. 497 - 506

Let Zα be a positive α‐stable random variable and \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$r\in {\mathbb...

60E15 | Mittag‐Leffler function | Bernstein function | Kanter function | unimodality | MSC 60E07 | 26A09 | Positive stable distribution | complete monotonicity | Unimodality | Mittag-Leffler function | Complete monotonicity | MATHEMATICS | Mathematics - Probability | Probability | Mathematics

60E15 | Mittag‐Leffler function | Bernstein function | Kanter function | unimodality | MSC 60E07 | 26A09 | Positive stable distribution | complete monotonicity | Unimodality | Mittag-Leffler function | Complete monotonicity | MATHEMATICS | Mathematics - Probability | Probability | Mathematics

Journal Article

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