The Special Functions and Their Approximations

Author: Yudell L. Luke
Publisher: Academic Press
ISBN: 9780080955605
Release Date: 1969
Genre: Mathematics

A detailed and self-contained and unified treatment of many mathematical functions which arise in applied problems, as well as the attendant mathematical theory for their approximations. many common features of the Bessel functions, Legendre functions, incomplete gamma functions, confluent hypergeometric functions, as well as of otherw, can be derived. Hitherto, many of the material upon which the volumes are based has been available only in papers scattered throughout the literature.

Essential Mathematical Methods for Physicists

Author: Hans-Jurgen Weber
Publisher: Academic Press
ISBN: 9780120598779
Release Date: 2004
Genre: Mathematics

This adaptation of Arfken and Weber's bestselling 'Mathematical Methods for Physicists' is a comprehensive, accessible reference for using mathematics to solve physics problems. Introductions and review material provide context and extra support for key ideas, with detailed examples.

Walter Gautschi Volume 1

Author: Claude Brezinski
Publisher: Springer Science & Business Media
ISBN: 9781461470342
Release Date: 2013-10-22
Genre: Mathematics

Walter Gautschi has written extensively on topics ranging from special functions, quadrature and orthogonal polynomials to difference and differential equations, software implementations, and the history of mathematics. He is world renowned for his pioneering work in numerical analysis and constructive orthogonal polynomials, including a definitive textbook in the former, and a monograph in the latter area. This three-volume set, Walter Gautschi: Selected Works with Commentaries, is a compilation of Gautschi’s most influential papers and includes commentaries by leading experts. The work begins with a detailed biographical section and ends with a section commemorating Walter’s prematurely deceased twin brother. This title will appeal to graduate students and researchers in numerical analysis, as well as to historians of science. Selected Works with Commentaries, Vol. 1 Numerical Conditioning Special Functions Interpolation and Approximation Selected Works with Commentaries, Vol. 2 Orthogonal Polynomials on the Real Line Orthogonal Polynomials on the Semicircle Chebyshev Quadrature Kronrod and Other Quadratures Gauss-type Quadrature Selected Works with Commentaries, Vol. 3 Linear Difference Equations Ordinary Differential Equations Software History and Biography Miscellanea Works of Werner Gautschi

Mathematical Methods For Physicists International Student Edition

Author: George B. Arfken
Publisher: Elsevier
ISBN: 9780080470696
Release Date: 2005-07-05
Genre: Science

This best-selling title provides in one handy volume the essential mathematical tools and techniques used to solve problems in physics. It is a vital addition to the bookshelf of any serious student of physics or research professional in the field. The authors have put considerable effort into revamping this new edition. Updates the leading graduate-level text in mathematical physics Provides comprehensive coverage of the mathematics necessary for advanced study in physics and engineering Focuses on problem-solving skills and offers a vast array of exercises Clearly illustrates and proves mathematical relations New in the Sixth Edition: Updated content throughout, based on users' feedback More advanced sections, including differential forms and the elegant forms of Maxwell's equations A new chapter on probability and statistics More elementary sections have been deleted

Hypergeometric Orthogonal Polynomials and Their q Analogues

Author: Roelof Koekoek
Publisher: Springer Science & Business Media
ISBN: 364205014X
Release Date: 2010-03-18
Genre: Mathematics

The present book is about the Askey scheme and the q-Askey scheme, which are graphically displayed right before chapter 9 and chapter 14, respectively. The fa- lies of orthogonal polynomials in these two schemes generalize the classical orth- onal polynomials (Jacobi, Laguerre and Hermite polynomials) and they have pr- erties similar to them. In fact, they have properties so similar that I am inclined (f- lowing Andrews & Askey [34]) to call all families in the (q-)Askey scheme classical orthogonal polynomials, and to call the Jacobi, Laguerre and Hermite polynomials very classical orthogonal polynomials. These very classical orthogonal polynomials are good friends of mine since - most the beginning of my mathematical career. When I was a fresh PhD student at the Mathematical Centre (now CWI) in Amsterdam, Dick Askey spent a sabbatical there during the academic year 1969–1970. He lectured to us in a very stimulating wayabouthypergeometricfunctionsandclassicalorthogonalpolynomials. Evenb- ter, he gave us problems to solve which might be worth a PhD. He also pointed out to us that there was more than just Jacobi, Laguerre and Hermite polynomials, for instance Hahn polynomials, and that it was one of the merits of the Higher Transc- dental Functions (Bateman project) that it included some newer stuff like the Hahn polynomials (see [198, §10. 23]).

Mathematical Functions and Their Approximations

Author: Yudell L. Luke
Publisher: Academic Press
ISBN: 9781483262451
Release Date: 2014-05-10
Genre: Mathematics

Mathematical Functions and their Approximations is an updated version of the Applied Mathematics Series 55 Handbook based on the 1954 Conference on Mathematical Tables, held at Cambridge, Massachusetts. The aim of the conference is to determine the need for mathematical tables in view of the availability of high speed computing machinery. This work is composed of 14 chapters that cover the machinery for the expansion of the generalized hypergeometric function and other functions in infinite series of Jacobi and Chebyshev polynomials of the first kind. Numerical coefficients for Chebyshev expansions of the more common functions are tabulated. Other chapters contain polynomial and rational approximations for certain class of G-functions, the coefficients in the early polynomials of these rational approximations, and the Padé approximations for many of the elementary functions and the incomplete gamma functions. The remaining chapters describe the development of analytic approximations and expansions. This book will prove useful to mathematicians, advance mathematics students, and researchers.

Approximation Theory VIII

Author: C K Chui
Publisher: World Scientific
ISBN: 9789814549066
Release Date: 1995-11-07
Genre: Mathematics

' This is the collection of the refereed and edited papers presented at the 8th Texas International Conference on Approximation Theory. It is interdisciplinary in nature and consists of two volumes. The central theme of Vol. I is the core of approximation theory. It includes such important areas as qualitative approximations, interpolation theory, rational approximations, radial-basis functions, and splines. The second volume focuses on topics related to wavelet analysis, including multiresolution and multi-level approximation, subdivision schemes in CAGD, and applications. Contents:Volume I:Differentiated Shift-Invariant Integral Operators (G A Anastassiou)Efficient Matrix Methods for the True Least-Squares Approximation of Structured Multivariate Data (I J Anderson & J C Mason)Vectorially Minimal Projections (A Bacopoulos & B L Chalmers)Error of an Arbitrary Order for the Approximate Solution of Systems of nth Order Differential Equations with Spline Functions (B S Badr et al)A Note on Irving Glicksberg''s Pseudocompactness Papers (J Blatter & H König)A Multivariate Divided Difference (C de Boor)Approximation Using Positive Definite Functions (E W Cheney)A Brief Glance at the Research of Ward Cheney (W Light)Ideas of Weighted Polynomial Approximation on (-∞,∞) (D S Lubinsky)Piecewise Convex Function Estimation and Model Selection (K S Riedel)Multivariate Interpolation and Approximation by Translates of a Basis Function (R Schaback)and other papersVolume II:A Wavelet-Like Unconditional Basis (K–F Chang)Multivariate Interpolating Wavelets (C K Chui & C Li)Nonlinear Wavelet Approximation and Image Compression (A Cohen)Wavelets and Interactive Surface Modeling (E Cornea et al)Multiscale Analysis, Approximation, and the Interpolation Spaces (W Dahmen)Using Fredholm Determinants to Estimate the Smoothness of Refinable Functions (I Daubechies)Stability and Independence of the Shifts of a Multivariate Refinable Function (T Hogan)Refinable Shift-Invariant Spaces: From Splines to Wavelets (R Q Jia)Weakly Singular Fredholm Integral Equations I: Singularity Preserving Wavelet-Galerkin Methods (C A Micchelli & Y–S Xu)and other papers Readership: Applied mathematicians. Keywords:Proceedings;Conference;Approximation Theory;College Station, TX (USA);Interpolation;Wavelets;Multilevel Approximation'

Series of Faber Polynomials

Author: P.K. Suetin
Publisher: CRC Press
ISBN: 9056990586
Release Date: 1998-03-23
Genre: Mathematics

Presents some important classical and modern results of the series of Faber polynomials and their applications. Interest in this subject has increased rapidly over the last decade, although the presentation of research has, until now, been confined mainly to journal articles. Applications include theory of functions of complex variables, theory of analytic function approximation, and some aspects of numerical analysis.