Constructive approximation, ISSN 1432-0940, 2015, Volume 43, Issue 3, pp. 357 - 369

Littlewood polynomials are polynomials with each of their coefficients in $$\{-1,1\}$$ { - 1 , 1 } . A sequence of Littlewood polynomials that satisfies a...

11C08 | 05D99 | 33E99 | Numerical Analysis | Analysis | Littlewood polynomials | Rudin–Shapiro polynomials | 41A10 | 11B75 | 11P99 | Mathematics | Mahler measure | SUBARCS | MATHEMATICS | BOUNDS | NORM | Rudin-Shapiro polynomials | FEKETE POLYNOMIALS | MOMENTS

11C08 | 05D99 | 33E99 | Numerical Analysis | Analysis | Littlewood polynomials | Rudin–Shapiro polynomials | 41A10 | 11B75 | 11P99 | Mathematics | Mahler measure | SUBARCS | MATHEMATICS | BOUNDS | NORM | Rudin-Shapiro polynomials | FEKETE POLYNOMIALS | MOMENTS

Journal Article

Foundations of computational mathematics, ISSN 1615-3383, 2012, Volume 13, Issue 4, pp. 615 - 666

Exceptional orthogonal polynomial systems (X-OPSs) arise as eigenfunctions of Sturm–Liouville problems, but without the assumption that an eigenpolynomial of...

34A05 | Economics general | 33E99 | 33C4 | Darboux–Crum transformation | Linear and Multilinear Algebras, Matrix Theory | Mathematics | Numerical Analysis | 34A30 | Applications of Mathematics | Math Applications in Computer Science | Bochner theorem | Computer Science, general | Exceptional orthogonal polynomials | Sturm–Liouville problems | Darboux-Crum transformation | Sturm-Liouville problems | MATHEMATICS, APPLIED | SUPERSYMMETRY | DIFFERENTIAL-EQUATION | X-L LAGUERRE | QUASI-EXACT SOLVABILITY | MATHEMATICS | SHAPE-INVARIANT POTENTIALS | COMPUTER SCIENCE, THEORY & METHODS | DARBOUX TRANSFORMATIONS | OPERATORS | Theorems (Mathematics) | Eigenfunctions | Polynomials | Research | Theorems | Computational mathematics | Eigen values | Foundations | Computation | Classification | Byproducts | Mathematical models | Transformations

34A05 | Economics general | 33E99 | 33C4 | Darboux–Crum transformation | Linear and Multilinear Algebras, Matrix Theory | Mathematics | Numerical Analysis | 34A30 | Applications of Mathematics | Math Applications in Computer Science | Bochner theorem | Computer Science, general | Exceptional orthogonal polynomials | Sturm–Liouville problems | Darboux-Crum transformation | Sturm-Liouville problems | MATHEMATICS, APPLIED | SUPERSYMMETRY | DIFFERENTIAL-EQUATION | X-L LAGUERRE | QUASI-EXACT SOLVABILITY | MATHEMATICS | SHAPE-INVARIANT POTENTIALS | COMPUTER SCIENCE, THEORY & METHODS | DARBOUX TRANSFORMATIONS | OPERATORS | Theorems (Mathematics) | Eigenfunctions | Polynomials | Research | Theorems | Computational mathematics | Eigen values | Foundations | Computation | Classification | Byproducts | Mathematical models | Transformations

Journal Article

Constructive Approximation, ISSN 0176-4276, 2/2014, Volume 39, Issue 1, pp. 75 - 83

Painlevé equations are studied on the basis of linear equations, which are generic for them. Different possible approaches are compared to each other. Formulas...

Heun deformed equation | 33E99 | Mathematics | Heun equation | 2×2 Fuchsian linear system | 33E17 | Euler integral transform | Antiquantization | 32S99 | Apparent singularity | Numerical Analysis | Analysis | 81R12 | Painlevé equation | 34B30

Heun deformed equation | 33E99 | Mathematics | Heun equation | 2×2 Fuchsian linear system | 33E17 | Euler integral transform | Antiquantization | 32S99 | Apparent singularity | Numerical Analysis | Analysis | 81R12 | Painlevé equation | 34B30

Journal Article

Aequationes mathematicae, ISSN 0001-9054, 8/2015, Volume 89, Issue 4, pp. 957 - 980

By differentiations we derive from the functional equation $$\varphi (F(x)+G(y))+\psi (H(x)+K(y))-\omega (x+y)=0 \quad \quad \quad \quad (1)$$ φ ( F ( x ) + G...

Sutô sum | Mathematics | Secondary 33E99 | Analytic function | Maple worksheet | Equivalent solutions | Lambert W-function | 39B12 | Analysis | Primary 39B32 | Rank (linear) | Affine function | List | Symmetries | Combinatorics | Solution | Sutǒ sum | Linear equations

Sutô sum | Mathematics | Secondary 33E99 | Analytic function | Maple worksheet | Equivalent solutions | Lambert W-function | 39B12 | Analysis | Primary 39B32 | Rank (linear) | Affine function | List | Symmetries | Combinatorics | Solution | Sutǒ sum | Linear equations

Journal Article

Integral Transforms and Special Functions, ISSN 1065-2469, 08/2012, Volume 23, Issue 8, pp. 581 - 593

We show that many functions containing the Lambert W function are Stieltjes functions. We extend the known properties of the set of Stieltjes functions and...

Secondary: 26A48 | Lambert W function | complete Bernstein functions | completely monotonic functions | Primary: 33E99 | Bernstein functions | Stieltjes functions | MATHEMATICS | MATHEMATICS, APPLIED | PADE APPROXIMANTS | Integrals | Transforms | Representations

Secondary: 26A48 | Lambert W function | complete Bernstein functions | completely monotonic functions | Primary: 33E99 | Bernstein functions | Stieltjes functions | MATHEMATICS | MATHEMATICS, APPLIED | PADE APPROXIMANTS | Integrals | Transforms | Representations

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

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

Open Mathematics, ISSN 2391-5455, 02/2019, Volume 17, Issue 1, pp. 32 - 42

Given positive integers , ′ and , we investigate the Möbius-Bernoulli numbers ), double Möbius-Bernoulli numbers (n, ′), and Möbius-Bernoulli polynomials )( )....

Möbius-Bernoulli numbers | Barnes-Bernoulli numbers | 33E99 | Dedekind sums | 11A05 | Mobius-Bernoulli numbers | MATHEMATICS | CRITICAL-VALUES | möbius-bernoulli numbers | 33e99 | barnes-bernoulli numbers | 11a05 | dedekind sums

Möbius-Bernoulli numbers | Barnes-Bernoulli numbers | 33E99 | Dedekind sums | 11A05 | Mobius-Bernoulli numbers | MATHEMATICS | CRITICAL-VALUES | möbius-bernoulli numbers | 33e99 | barnes-bernoulli numbers | 11a05 | dedekind sums

Journal Article

Abstract and Applied Analysis, ISSN 1085-3375, 04/2004, Volume 2004, Issue 4, pp. 295 - 306

Journal Article

Moroccan Journal of Pure and Applied Analysis, 06/2018, Volume 4, Issue 1, pp. 17 - 32

In this paper the periodic even functions for which all the regular Riemann sums vanishe are called special periodic even functions. A construction of some of...

fonctions de Moebius et de Liouville | estimation de H. Davenport | Primary: 33E99 | éries de Fourier

fonctions de Moebius et de Liouville | estimation de H. Davenport | Primary: 33E99 | éries de Fourier

Journal Article

Osaka journal of mathematics, ISSN 0030-6126, 12/1996, Volume 33, Issue 4, pp. 927 - 949

Journal Article

12.
Full Text
Boundary Value Problem for Matrix Analogue of Helmholtz’s Equation (Poincaré’s Problem)

Mediterranean journal of mathematics, ISSN 1660-5454, 2018, Volume 15, Issue 3, pp. 1 - 11

In this paper, a system of equations in partial derivatives of elliptic type (1.1) is considered in $$E^2$$ E2 space of the complex variable $$z=x+iy$$ z=x+iy...

Elliptic systems | 33E99 | Noether’s theorems | integral systems | Mathematics, general | Mathematics | 33E05 | 45E05 | special functions | MATHEMATICS | MATHEMATICS, APPLIED | Noether's theorems

Elliptic systems | 33E99 | Noether’s theorems | integral systems | Mathematics, general | Mathematics | 33E05 | 45E05 | special functions | MATHEMATICS | MATHEMATICS, APPLIED | Noether's theorems

Journal Article

Advances in Computational Mathematics, ISSN 1019-7168, 1/2008, Volume 28, Issue 1, pp. 63 - 79

Two integrals (3.6), (4.7) for the period of a periodic solution of the Lotka–Volterra system are presented in terms of two inverse functions of $x\exp(x)$...

Gauss–Chebyshev integration rule of the first kind | 34C15 | period | 33E99 | Numeric Computing | midpoint rule | Theory of Computation | Algebra | Calculus of Variations and Optimal Control; Optimization | Lotka–Volterra system | 65D32 | Computer Science | Lambert’s W function | Mathematics, general | Midpoint rule | Period | Gauss-Chebyshev integration rule of the first kind | Lotka-Volterra system | Lambert's W function | MATHEMATICS, APPLIED | SINGULAR FUNCTIONS | REAL | TRAPEZOIDAL QUADRATURE-RULES | MODEL | OSCILLATIONS

Gauss–Chebyshev integration rule of the first kind | 34C15 | period | 33E99 | Numeric Computing | midpoint rule | Theory of Computation | Algebra | Calculus of Variations and Optimal Control; Optimization | Lotka–Volterra system | 65D32 | Computer Science | Lambert’s W function | Mathematics, general | Midpoint rule | Period | Gauss-Chebyshev integration rule of the first kind | Lotka-Volterra system | Lambert's W function | MATHEMATICS, APPLIED | SINGULAR FUNCTIONS | REAL | TRAPEZOIDAL QUADRATURE-RULES | MODEL | OSCILLATIONS

Journal Article

Integral transforms and special functions, ISSN 1476-8291, 2018, Volume 29, Issue 12, pp. 1001 - 1017

We obtain some new formulae to compute the first derivative of confluent and biconfluent Heun functions under the minimal assumption of fixing only one...

triconfluent Heun function | Special functions | Heun confluent function | doubly confluent Heun function | biconfluent Heun function | 33E99 | 33C55 | 34A99 | 33E05 | 33C05 | 70H03 | MATHEMATICS | MATHEMATICS, APPLIED | Ordinary differential equations | Integrals | Differential equations

triconfluent Heun function | Special functions | Heun confluent function | doubly confluent Heun function | biconfluent Heun function | 33E99 | 33C55 | 34A99 | 33E05 | 33C05 | 70H03 | MATHEMATICS | MATHEMATICS, APPLIED | Ordinary differential equations | Integrals | Differential equations

Journal Article

Integral Transforms and Special Functions, ISSN 1065-2469, 10/2018, Volume 29, Issue 10, pp. 794 - 804

We present a conspicuous number of indefinite integrals involving Heun functions and their products obtained by means of the Lagrangian formulation of a...

hypergeometric functions | Special functions | complete elliptic integrals | Heun functions | 33E99 | 33C55 | 34A99 | 33E05 | 33C05 | 70H03 | MATHEMATICS | MATHEMATICS, APPLIED | Hypergeometric functions | Ordinary differential equations | Elliptic functions | Integrals | Differential equations

hypergeometric functions | Special functions | complete elliptic integrals | Heun functions | 33E99 | 33C55 | 34A99 | 33E05 | 33C05 | 70H03 | MATHEMATICS | MATHEMATICS, APPLIED | Hypergeometric functions | Ordinary differential equations | Elliptic functions | Integrals | Differential equations

Journal Article

Integral Transforms and Special Functions, ISSN 1065-2469, 01/2018, Volume 29, Issue 1, pp. 1 - 15

The goal of this paper is to establish a more generalized Cameron-Storvick theorem with respect to the conditional generalized integral transform (CGIT) and...

bounded linear operator | Gaussian process | first variation | Cameron-Storvick theorem | Conditional generalized integral transform | Cameron–Storvick theorem | 28C20 | MATHEMATICS, APPLIED | 33E99 | 44A20 | 44A15 | MATHEMATICS | ANALYTIC FEYNMAN-INTEGRALS | PRODUCT | FUNCTIONALS | TRANSFORMS | Operators (mathematics) | Theorems | Function space | Functionals | Integral transforms | Linear operators

bounded linear operator | Gaussian process | first variation | Cameron-Storvick theorem | Conditional generalized integral transform | Cameron–Storvick theorem | 28C20 | MATHEMATICS, APPLIED | 33E99 | 44A20 | 44A15 | MATHEMATICS | ANALYTIC FEYNMAN-INTEGRALS | PRODUCT | FUNCTIONALS | TRANSFORMS | Operators (mathematics) | Theorems | Function space | Functionals | Integral transforms | Linear operators

Journal Article

Analysis Mathematica, ISSN 0133-3852, 12/2016, Volume 42, Issue 4, pp. 387 - 400

This paper is concentrated on giving a module containment theorem for piecewise continuous almost periodic functions (pcap function for short). One first...

33E99 | Kronecker’s theorem | Analysis | module | Mathematics | 34K14 | (piecewise continuous) almost periodic function | impulsive differential equation | MATHEMATICS | Kronecker's theorem | MODEL | Differential equations | Functions (mathematics) | Theorems | Periodic functions | Mathematical analysis | Modules | Translations | Continuity (mathematics) | Containment

33E99 | Kronecker’s theorem | Analysis | module | Mathematics | 34K14 | (piecewise continuous) almost periodic function | impulsive differential equation | MATHEMATICS | Kronecker's theorem | MODEL | Differential equations | Functions (mathematics) | Theorems | Periodic functions | Mathematical analysis | Modules | Translations | Continuity (mathematics) | Containment

Journal Article

Duke Mathematical Journal, ISSN 0012-7094, 1993, Volume 70, Issue 3, pp. 481 - 516

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

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

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

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