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The Table of Integrals, Series, and Products is the major reference source for integrals in the English language.It is designed for use by mathematicians, scientists, and professional engineers who need to solve complex mathematical problems.*Completely reset edition of Gradshteyn and Ryzhik reference book*New entries and sections kept in orginal numbering system with an expanded bibliography*Enlargement of material on orthogonal polynomials, theta functions, Laplace and Fourier transform pairs and much more.orthogonal polynomials, theta functions, Laplace and Fourier tr

Functional analysis --- Mathematics --- Mathématiques --- Tables. --- Tables --- 517.58 --- 517.3 --- 519.66 --- -Math --- Science --- 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. --- Integral calculus. Integration --- Mathematic tables and their compilation --- -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. --- 519.66 Mathematic tables and their compilation --- 517.3 Integral calculus. Integration --- 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. --- -519.66 Mathematic tables and their compilation --- Math --- 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 --- Logarithms. --- Logs (Logarithms) --- Algebra --- Mathematics - Tables

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Polynomials --- Approximation theory --- Algebra --- Theory of approximation --- Functional analysis --- Functions --- Chebyshev systems

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Stochastic processes --- Orthogonal polynomials --- Processus stochastiques --- Polynômes orthogonaux --- 519.216 --- Academic collection --- 517.518.8 --- Random processes --- Probabilities --- Fourier analysis --- Functions, Orthogonal --- Polynomials --- Stochastic processes in general. Prediction theory. Stopping times. Martingales --- Approximation of functions by polynomials and their generalizations --- Orthogonal polynomials. --- Stochastic processes. --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- 517.518.8 Approximation of functions by polynomials and their generalizations --- 519.216 Stochastic processes in general. Prediction theory. Stopping times. Martingales --- Polynômes orthogonaux --- Probabilities. --- Probability Theory and Stochastic Processes. --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Fonctions speciales --- Polynomes orthogonaux

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Orthogonal polynomials. --- Random matrices. --- Functions of complex variables --- Riemann-Hilbert problems --- Fonctions d'une variable complexe --- Riemann-Hilbert, Problèmes de --- Functions of complex variables. --- Riemann-Hilbert problems. --- Riemann-Hilbert, Problèmes de --- Fonctions speciales --- Polynomes orthogonaux

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We study in Part I of this monograph the computational aspect of almost all moduli of continuity over wide classes of functions exploiting some of their convexity properties. To our knowledge it is the first time the entire calculus of moduli of smoothness has been included in a book. We then present numerous applications of Approximation Theory, giving exact val­ ues of errors in explicit forms. The K-functional method is systematically avoided since it produces nonexplicit constants. All other related books so far have allocated very little space to the computational aspect of moduli of smoothness. In Part II, we study/examine the Global Smoothness Preservation Prop­ erty (GSPP) for almost all known linear approximation operators of ap­ proximation theory including: trigonometric operators and algebraic in­ terpolation operators of Lagrange, Hermite-Fejer and Shepard type, also operators of stochastic type, convolution type, wavelet type integral opera­ tors and singular integral operators, etc. We present also a sufficient general theory for GSPP to hold true. We provide a great variety of applications of GSPP to Approximation Theory and many other fields of mathemat­ ics such as Functional analysis, and outside of mathematics, fields such as computer-aided geometric design (CAGD). Most of the time GSPP meth­ ods are optimal. Various moduli of smoothness are intensively involved in Part II. Therefore, methods from Part I can be used to calculate exactly the error of global smoothness preservation. It is the first time in the literature that a book has studied GSPP.

Smoothness of functions --- Moduli theory --- Approximation theory --- 517.518.8 --- Smooth functions --- Functions --- Theory of moduli --- Analytic spaces --- Functions of several complex variables --- Geometry, Algebraic --- Theory of approximation --- Functional analysis --- Polynomials --- Chebyshev systems --- Approximation of functions by polynomials and their generalizations --- Approximation theory. --- Moduli theory. --- Smoothness of functions. --- 517.518.8 Approximation of functions by polynomials and their generalizations --- Applied mathematics. --- Engineering mathematics. --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Mathematical analysis. --- Analysis (Mathematics). --- Computer mathematics. --- Applications of Mathematics. --- Approximations and Expansions. --- Global Analysis and Analysis on Manifolds. --- Analysis. --- Computational Mathematics and Numerical Analysis. --- Computer mathematics --- Electronic data processing --- Mathematics --- 517.1 Mathematical analysis --- Mathematical analysis --- Geometry, Differential --- Topology --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Engineering --- Engineering analysis