## Progress in approximation theory: an international perspectiveDesigned to give a contemporary international survey of research activities in approximation theory and special functions, this book brings together the work of approximation theorists from North America, Western Europe, Asia, Russia, the Ukraine, and several other former Soviet countries. Contents include: results dealing with q-hypergeometric functions, differencehypergeometric functions and basic hypergeometric series with Schur function argument; the theory of orthogonal polynomials and expansions, including generalizations of SzegA type asymptotics and connections with Jacobi matrices; the convergence theory for PadA(c) and Hermite-PadA(c) approximants, with emphasis on techniques from potential theory; material on wavelets and fractals and their relationship to invariant measures and nonlinear approximation; generalizations of de Brange's in equality for univalent functions in a quasi-orthogonal Hilbert space setting; applications of results concerning approximation by entire functions and the problem of analytic continuation; and other topics. |

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### Contents

Difference Hypergeometric Functions | 1 |

Pad6 Approximants for Some Hypergeometric Functions | 37 |

Summation Theorems for Basic Hypergeometric Series | 51 |

Copyright | |

14 other sections not shown

### Other editions - View all

Progress in Approximation Theory: An International Perspective A.A. Gonchar,E.B. Saff Limited preview - 2012 |

### Common terms and phrases

A.A. Gonchar algebraic Amer analytic continuation Angelesco apply Approx APPROXIMATION THEORY arbitrary Askey Askey-Wilson polynomials assume asymptotics basic hypergeometric series Blaschke product Chebyshev polynomials classical coefficients compact subsets condition conjecture consider constant construction continuous function convergence corresponding cubes defined definition denote Department of Mathematics domain E.B. Saff English transl entire function equation estimate exists finite formula Fourier transform func given Hence Hermite-Pade polynomials holomorphic homogeneous implies inequality integral interpolation interval Jacobi matrix Lebesgue Lemma linear Math method Nevai Nikishin obtain orthogonal polynomials Pade approximants Padi poles probability measure problem PROGRESS IN APPROXIMATION proof of Theorem properties Proposition proved rational approximants rational functions relations Riemann Riemann surface satisfies Schur function Section segment sequence solutions space Theorem 3.1 tions uniformly unique University wavelet weight function Wilson polynomials zeros