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Number theory. --- Combinatorial analysis. --- Functions, Special.
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Mathematical analysis --- Functions, Special --- Mathematical physics --- Physical mathematics --- Physics --- Special functions --- Mathematics --- Functions, Special. --- Mathematical physics. --- Monograph
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Bessel functions --- Functions, Special --- Fonctions spéciales --- Bessel, Fonctions de --- Nuclear physics --- Solid state physics --- Wave propagation
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Mathematical analysis --- Mathematical physics --- Functions, Special --- 517.5 --- Special functions --- Theory of functions --- Functions, Special. --- 517.5 Theory of functions --- Hypergeometric functions. --- Fonctions hypergéométriques. --- Analyse mathématique --- Fonctions hypergéométriques --- Analyse mathématique --- Mathematical analysis. --- Fonctions speciales --- Polynomes orthogonaux --- Fonctions de legendre --- Harmoniques spheriques --- Fonctions de bessel
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Harmonic analysis. Fourier analysis --- 517.9 --- Functions, Special --- Harmonic analysis --- Lie groups --- Locally compact groups --- Compact groups --- Topological groups --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Special functions --- Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- 517.9 Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- Fonctions spéciales --- Analyse harmonique --- Groupes de Lie --- Groupes localement compacts --- Locally compact groups. --- Lie groups. --- Functions, Special. --- Harmonic analysis. --- Mathématiques --- Lie, Groupes de --- Fonctions speciales --- Groupes topologiques
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Special functions and orthogonal polynomials in particular have been around for centuries. Can you imagine mathematics without trigonometric functions, the exponential function or polynomials? In the twentieth century the emphasis was on special functions satisfying linear differential equations, but this has now been extended to difference equations, partial differential equations and non-linear differential equations. The present set of lecture notes containes seven chapters about the current state of orthogonal polynomials and special functions and gives a view on open problems and future directions. The topics are: computational methods and software for quadrature and approximation, equilibrium problems in logarithmic potential theory, discrete orthogonal polynomials and convergence of Krylov subspace methods in numerical linear algebra, orthogonal rational functions and matrix orthogonal rational functions, orthogonal polynomials in several variables (Jack polynomials) and separation of variables, a classification of finite families of orthogonal polynomials in Askey’s scheme using Leonard pairs, and non-linear special functions associated with the Painlevé equations.
Orthogonal polynomials. --- Functions, Special. --- Polynômes orthogonaux --- Fonctions spéciales --- Orthogonal polynomials --- Functions, Special --- Operations Research --- Mathematical Theory --- Civil & Environmental Engineering --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- 517.518.8 --- 517.58 --- Approximation of functions by polynomials and their generalizations --- Special functions. Hyperbolic functions. Euler integrals. Gamma functions. Elliptic functions and integrals. Bessel functions. Other cylindrical functions. Spherical functions. Legendre polynomials. Orthogonal polynomials. Chebyshev polynomials. --- 517.58 Special functions. Hyperbolic functions. Euler integrals. Gamma functions. Elliptic functions and integrals. Bessel functions. Other cylindrical functions. Spherical functions. Legendre polynomials. Orthogonal polynomials. Chebyshev polynomials. --- 517.518.8 Approximation of functions by polynomials and their generalizations --- Special functions --- Mathematics. --- Approximation theory. --- Fourier analysis. --- Special functions. --- Numerical analysis. --- Approximations and Expansions. --- Special Functions. --- Numerical Analysis. --- Fourier Analysis. --- Fourier analysis --- Functions, Orthogonal --- Polynomials --- Mathematical analysis --- Special functions. Hyperbolic functions. Euler integrals. Gamma functions. Elliptic functions and integrals. Bessel functions. Other cylindrical functions. Spherical functions. Legendre polynomials. Orthogonal polynomials. Chebyshev polynomials --- Analysis, Fourier --- Theory of approximation --- Functional analysis --- Functions --- Chebyshev systems --- Math --- Science --- Functions, special.
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Functions, Special --- Orthogonal polynomials --- Academic collection --- 517.518.8 --- 517.518.8 Approximation of functions by polynomials and their generalizations --- Approximation of functions by polynomials and their generalizations --- Special functions --- Fourier analysis --- Functions, Orthogonal --- Polynomials --- Mathematical analysis --- Special functions. --- Computer mathematics. --- Topological groups. --- Lie groups. --- Combinatorics. --- Differential equations. --- Fourier analysis. --- Special Functions. --- Computational Science and Engineering. --- Topological Groups, Lie Groups. --- Ordinary Differential Equations. --- Fourier Analysis. --- Analysis, Fourier --- 517.91 Differential equations --- Differential equations --- Combinatorics --- Algebra --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Groups, Topological --- Continuous groups --- Computer mathematics --- Electronic data processing --- Mathematics
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