2001, ISBN 9810243537, xx, 195

Book

1992, 2nd ed., ISBN 0070018480, xix, 479

Book

1996, ISBN 9780471113133, xii, 374

This book gives an introduction to the classical, well-known special functions which play a role in mathematical physics, especially in boundary value problems...

Functions, Special | Boundary value problems | Mathematical physics

Functions, Special | Boundary value problems | Mathematical physics

Book

Journal of Computational Physics, ISSN 0021-9991, 12/2017, Volume 350, pp. 326 - 342

We express a certain complex-valued solution of Legendre's differential equation as the product of an oscillatory exponential function and an integral involving only nonoscillatory elementary functions...

Nonoscillatory phase functions | Fast algorithms | Special functions | NODES | GAUSS-LEGENDRE | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | EXPANSIONS | WEIGHTS | COMPUTATION | PHYSICS, MATHEMATICAL | Differential equations | Computer science | Algorithms | DIFFERENTIAL EQUATIONS | LEGENDRE POLYNOMIALS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | ASYMPTOTIC SOLUTIONS

Nonoscillatory phase functions | Fast algorithms | Special functions | NODES | GAUSS-LEGENDRE | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | EXPANSIONS | WEIGHTS | COMPUTATION | PHYSICS, MATHEMATICAL | Differential equations | Computer science | Algorithms | DIFFERENTIAL EQUATIONS | LEGENDRE POLYNOMIALS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | ASYMPTOTIC SOLUTIONS

Journal Article

Foundations of Computational Mathematics, ISSN 1615-3375, 4/2019, Volume 19, Issue 2, pp. 297 - 331

This paper examines the problem of extrapolation of an analytic function for $$x > 1$$ x > 1 given $$N+1$$ N + 1 perturbed samples from an equally spaced grid...

Linear and Multilinear Algebras, Matrix Theory | Mathematics | Extrapolation | Interpolation | Numerical Analysis | 41A10 | 65D05 | Approximation theory | Applications of Mathematics | Math Applications in Computer Science | Computer Science, general | Legendre polynomials | Economics, general | Chebyshev polynomials | MATHEMATICS | MATHEMATICS, APPLIED | COMPUTER SCIENCE, THEORY & METHODS | Functions | Research | Functional equations | Mathematical research | Perturbation (Mathematics) | Stability | Approximation | Analytic functions | Asymptotic properties | Mathematical analysis | Chebyshev approximation | Polynomials | Oversampling | Smoothness

Linear and Multilinear Algebras, Matrix Theory | Mathematics | Extrapolation | Interpolation | Numerical Analysis | 41A10 | 65D05 | Approximation theory | Applications of Mathematics | Math Applications in Computer Science | Computer Science, general | Legendre polynomials | Economics, general | Chebyshev polynomials | MATHEMATICS | MATHEMATICS, APPLIED | COMPUTER SCIENCE, THEORY & METHODS | Functions | Research | Functional equations | Mathematical research | Perturbation (Mathematics) | Stability | Approximation | Analytic functions | Asymptotic properties | Mathematical analysis | Chebyshev approximation | Polynomials | Oversampling | Smoothness

Journal Article

Automatica, ISSN 0005-1098, 01/2015, Volume 51, pp. 308 - 317

The time-variant frequency response function (TV-FRF) uniquely characterises the dynamic behaviour of a linear time-variant (LTV) system...

Legendre polynomials | Time-variant systems | Arbitrary excitations | Time-variant frequency response function | Nonparametric estimates | VARYING SYSTEMS | VIBRATION | VALIDATION | INPUTS | IDENTIFICATION | ENGINEERING, ELECTRICAL & ELECTRONIC | DYNAMICS | HYBRID SYSTEMS | AUTOMATION & CONTROL SYSTEMS | Automation | Dynamics | Estimating | Mathematical models | Polynomials | Excitation | Estimates | Dynamical systems | Frequency response functions

Legendre polynomials | Time-variant systems | Arbitrary excitations | Time-variant frequency response function | Nonparametric estimates | VARYING SYSTEMS | VIBRATION | VALIDATION | INPUTS | IDENTIFICATION | ENGINEERING, ELECTRICAL & ELECTRONIC | DYNAMICS | HYBRID SYSTEMS | AUTOMATION & CONTROL SYSTEMS | Automation | Dynamics | Estimating | Mathematical models | Polynomials | Excitation | Estimates | Dynamical systems | Frequency response functions

Journal Article

9.
Full Text
Two-dimensional charged particle image inversion using a polar basis function expansion

Review of scientific instruments, ISSN 1089-7623, 2004, Volume 75, Issue 11, pp. 4989 - 4996

We present an inversion method called pBasex aimed at reconstructing the original Newton sphere of expanding charged particles from its two-dimensional projection by fitting a set of basis functions...

PHOTOIONIZATION | INSTRUMENTS & INSTRUMENTATION | PHYSICS, APPLIED | CIRCULAR-DICHROISM | ANGULAR-DISTRIBUTION | PRODUCTS | PHOTOELECTRON | IONS | EMISSION | IONIZATION | MOLECULES | LEGENDRE POLYNOMIALS | IMAGE PROCESSING | PHOTOELECTRON SPECTROSCOPY | SPATIAL RESOLUTION | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | IMAGES | CHARGED PARTICLES | PERFORMANCE | NOISE | ALGORITHMS | ACCURACY

PHOTOIONIZATION | INSTRUMENTS & INSTRUMENTATION | PHYSICS, APPLIED | CIRCULAR-DICHROISM | ANGULAR-DISTRIBUTION | PRODUCTS | PHOTOELECTRON | IONS | EMISSION | IONIZATION | MOLECULES | LEGENDRE POLYNOMIALS | IMAGE PROCESSING | PHOTOELECTRON SPECTROSCOPY | SPATIAL RESOLUTION | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | IMAGES | CHARGED PARTICLES | PERFORMANCE | NOISE | ALGORITHMS | ACCURACY

Journal Article

Journal of dynamic systems, measurement, and control, ISSN 1528-9028, 2018, Volume 140, Issue 1

In this paper, a simple model-free controller for electrically driven robot manipulators is presented using function approximation techniques (FAT...

robot manipulator | REGRESSOR MATRIX | DESIGN | UNCERTAINTIES | ELECTRICALLY-DRIVEN ROBOTS | neuro-fuzzy control | adaptive control | permanent magnet DC motor | Fourier series | function approximation techniques | TRACKING CONTROL | INSTRUMENTS & INSTRUMENTATION | NONLINEAR-SYSTEMS | OBSERVER | Legendre polynomials | FUZZY CONTROL | AUTOMATION & CONTROL SYSTEMS

robot manipulator | REGRESSOR MATRIX | DESIGN | UNCERTAINTIES | ELECTRICALLY-DRIVEN ROBOTS | neuro-fuzzy control | adaptive control | permanent magnet DC motor | Fourier series | function approximation techniques | TRACKING CONTROL | INSTRUMENTS & INSTRUMENTATION | NONLINEAR-SYSTEMS | OBSERVER | Legendre polynomials | FUZZY CONTROL | AUTOMATION & CONTROL SYSTEMS

Journal Article

Journal of mathematical analysis and applications, ISSN 0022-247X, 2019, Volume 477, Issue 2, pp. 1328 - 1352

... of binomial coefficients and the Franel numbers by means of suitable generating functions and hypergeometric function...

Franel numbers | Bernoulli and Euler numbers and polynomials | Mirimanoff polynomial | Legendre polynomial | p-adic integrals | Generating functions | MATHEMATICS, APPLIED | BERNOULLI NUMBERS | IDENTITIES | Francl numbers | EULER NUMBERS | MATHEMATICS | ZETA | RECURRENCES | PRODUCTS

Franel numbers | Bernoulli and Euler numbers and polynomials | Mirimanoff polynomial | Legendre polynomial | p-adic integrals | Generating functions | MATHEMATICS, APPLIED | BERNOULLI NUMBERS | IDENTITIES | Francl numbers | EULER NUMBERS | MATHEMATICS | ZETA | RECURRENCES | PRODUCTS

Journal Article

Journal de mathématiques pures et appliquées, ISSN 0021-7824, 03/2014, Volume 101, Issue 3, pp. 303 - 329

.... In the present paper, we study the Riemannian distance function associated with the Heston model and obtain explicit formulas for this function using geometrical and analytical methods...

Grushin plane | Legendre–Fenchel transform | Limiting cumulant generating function | Heston model | Legendre-Fenchel transform | MATHEMATICS | MATHEMATICS, APPLIED | IMPLIED VOLATILITY | MODEL | EQUATION

Grushin plane | Legendre–Fenchel transform | Limiting cumulant generating function | Heston model | Legendre-Fenchel transform | MATHEMATICS | MATHEMATICS, APPLIED | IMPLIED VOLATILITY | MODEL | EQUATION

Journal Article

1966, 1st English ed., Mathematical tables series, v. 40, 107

Book

Boletim da Sociedade Paranaense de Matematica, ISSN 0037-8712, 2018, Volume 36, Issue 1, pp. 177 - 193

In the present work we derive various integral formulas involving ℵ-function multiplied with algebraic functions and special functions.

Jacobi polynomials | H-function | Bessel Maitland function | I-function | Aleph function | Hypergeometric function | Legendre function

Jacobi polynomials | H-function | Bessel Maitland function | I-function | Aleph function | Hypergeometric function | Legendre function

Journal Article

Journal of Machine Learning Research, ISSN 1532-4435, 09/2010, Volume 11, pp. 2423 - 2455

In this paper, we propose a general framework for sparse semi-supervised learning, which concerns using a small portion of unlabeled data and a few labeled data to represent target functions and thus...

Multi-view regularization | Representer theorem | Statistical learning theory | Fenchel-Legendre conjugate | Support vector machine | Semi-supervised learning | support vector machine | representer theorem | multiview regularization | statistical learning theory | semi-supervised learning | REGULARIZATION | AUTOMATION & CONTROL SYSTEMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Multi-view regularization | Representer theorem | Statistical learning theory | Fenchel-Legendre conjugate | Support vector machine | Semi-supervised learning | support vector machine | representer theorem | multiview regularization | statistical learning theory | semi-supervised learning | REGULARIZATION | AUTOMATION & CONTROL SYSTEMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Journal Article

Journal of Mathematical Chemistry, ISSN 0259-9791, 3/2018, Volume 56, Issue 3, pp. 825 - 849

... . We first construct an associated Legendre function expression for eigenfunctions of the Laplacian and use superposition principle to get a solution for the Laplace equation on $$\mathbf {H}^{n}$$ Hn...

33C45 | 35J05 | 35K15 | 35P10 | 44A20 | 47A10 | Hyperbolic upper half-space | 44A15 | Theoretical and Computational Chemistry | Poisson kernel | Chemistry | Physical Chemistry | Poincaré unit ball | Special functions | Associated Legendre function | Math. Applications in Chemistry | 42C05 | Poincare unit ball | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | EIGENFUNCTIONS | CHEMISTRY, MULTIDISCIPLINARY | Functions, Exponential | Analysis | Poisson processes

33C45 | 35J05 | 35K15 | 35P10 | 44A20 | 47A10 | Hyperbolic upper half-space | 44A15 | Theoretical and Computational Chemistry | Poisson kernel | Chemistry | Physical Chemistry | Poincaré unit ball | Special functions | Associated Legendre function | Math. Applications in Chemistry | 42C05 | Poincare unit ball | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | EIGENFUNCTIONS | CHEMISTRY, MULTIDISCIPLINARY | Functions, Exponential | Analysis | Poisson processes

Journal Article

Annals of Physics, ISSN 0003-4916, 06/2013, Volume 333, pp. 90 - 103

... to −5/4. As both are also bases of square-integrable functions, the universal enveloping algebra of so(3,2...

Square-integrable function | Special function | Lie algebra | PHYSICS, MULTIDISCIPLINARY | Algebra | LEGENDRE POLYNOMIALS | SPACE | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | ALGEBRA | LIE GROUPS | HARMONICS | SPHERICAL HARMONICS | IRREDUCIBLE REPRESENTATIONS

Square-integrable function | Special function | Lie algebra | PHYSICS, MULTIDISCIPLINARY | Algebra | LEGENDRE POLYNOMIALS | SPACE | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | ALGEBRA | LIE GROUPS | HARMONICS | SPHERICAL HARMONICS | IRREDUCIBLE REPRESENTATIONS

Journal Article

Journal of Vibration and Control, ISSN 1077-5463, 11/2018, Volume 24, Issue 21, pp. 5030 - 5043

In this paper, a numerical scheme based on hybrid Chelyshkov functions (HCFs) is presented to solve a class of fractional optimal control problems (FOCPs...

Fractional optimal control problems | fractional calculus | Gauss–Legendre quadrature | singular dynamic system | hybrid Chelyshkov functions | ACOUSTICS | MECHANICS | EQUATIONS | Gauss-Legendre quadrature | ENGINEERING, MECHANICAL | Economic models | Mathematical analysis | Optimal control | Iterative algorithms | Polynomials | Iterative methods | Dynamical systems

Fractional optimal control problems | fractional calculus | Gauss–Legendre quadrature | singular dynamic system | hybrid Chelyshkov functions | ACOUSTICS | MECHANICS | EQUATIONS | Gauss-Legendre quadrature | ENGINEERING, MECHANICAL | Economic models | Mathematical analysis | Optimal control | Iterative algorithms | Polynomials | Iterative methods | Dynamical systems

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 2009, Volume 71, Issue 12, pp. e103 - e108

We will solve the inhomogeneous Legendre’s differential equation and apply this result to estimate the error bound occurring when an analytic function...

Legendre function | Analytic function | Approximation | Legendre’s differential equation | Legendre's differential equation | MATHEMATICS | MATHEMATICS, APPLIED | Error analysis | Analytic functions | Mathematical analysis | Differential equations | Legendre functions | Nonlinearity | Estimates

Legendre function | Analytic function | Approximation | Legendre’s differential equation | Legendre's differential equation | MATHEMATICS | MATHEMATICS, APPLIED | Error analysis | Analytic functions | Mathematical analysis | Differential equations | Legendre functions | Nonlinearity | Estimates

Journal Article

1998, ISBN 9810235240, xiii, 150

Book

No results were found for your search.

Cannot display more than 1000 results, please narrow the terms of your search.