the special functions and their approximations volume 1

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The Special Functions And Their Approximations

Author : Yudell L. Luke
ISBN : 9780080955605
Genre : Mathematics
File Size : 89. 34 MB
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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.

The Special Functions And Their Approximations

Author : Yudell L. Luke
ISBN : UOM:39015000491244
Genre : Mathematics
File Size : 88. 46 MB
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Special Functions And Their Approximations

Author : Yudell L. Luke
ISBN : 9780080955612
Genre : Computers
File Size : 85. 23 MB
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Special Functions and Their Approximations: v. 2

Mathematical Functions And Their Approximations

Author : Yudell L. Luke
ISBN : 9781483262451
Genre : Mathematics
File Size : 54. 69 MB
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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.

The Special Functions And Their Approximations Vol 1 2

Author : Y. L. Luke
ISBN : OCLC:473344784
Genre :
File Size : 38. 84 MB
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Mathematics Of Approximation

Author : Johan de De Villiers
ISBN : 9789491216503
Genre : Mathematics
File Size : 89. 13 MB
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The approximation of a continuous function by either an algebraic polynomial, a trigonometric polynomial, or a spline, is an important issue in application areas like computer-aided geometric design and signal analysis. This book is an introduction to the mathematical analysis of such approximation, and, with the prerequisites of only calculus and linear algebra, the material is targeted at senior undergraduate level, with a treatment that is both rigorous and self-contained. The topics include polynomial interpolation; Bernstein polynomials and the Weierstrass theorem; best approximations in the general setting of normed linear spaces and inner product spaces; best uniform polynomial approximation; orthogonal polynomials; Newton-Cotes , Gauss and Clenshaw-Curtis quadrature; the Euler-Maclaurin formula ; approximation of periodic functions; the uniform convergence of Fourier series; spline approximation,with an extensive treatment of local spline interpolation,and its application in quadrature. Exercises are provided at the end of each chapter

Constructive Function Theory

Author : Isidor Pavlovich Natanson
ISBN : UOM:39015001338279
Genre : Approximation theory
File Size : 90. 72 MB
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Asymptotics And Special Functions

Author : F. W. J. Olver
ISBN : 9781483267449
Genre : Mathematics
File Size : 49. 56 MB
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Asymptotics and Special Functions provides a comprehensive introduction to two important topics in classical analysis: asymptotics and special functions. The integrals of a real variable and contour integrals are discussed, along with the Liouville-Green approximation and connection formulas for solutions of differential equations. Differential equations with regular singularities are also considered, with emphasis on hypergeometric and Legendre functions. Comprised of 14 chapters, this volume begins with an introduction to the basic concepts and definitions of asymptotic analysis and special functions, followed by a discussion on asymptotic theories of definite integrals containing a parameter. Contour integrals as well as integrals of a real variable are described. Subsequent chapters deal with the analytic theory of ordinary differential equations; differential equations with regular and irregular singularities; sums and sequences; and connection formulas for solutions of differential equations. The book concludes with an evaluation of methods used in estimating (as opposed to bounding) errors in asymptotic approximations and expansions. This monograph is intended for graduate mathematicians, physicists, and engineers.

Essential Mathematical Methods For Physicists

Author : Hans-Jurgen Weber
ISBN : 9780120598779
Genre : Mathematics
File Size : 49. 42 MB
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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.

Methods Of Mathematical Physics Volume 2

Author : Richard Courant
ISBN : 9783527617241
Genre : Science
File Size : 61. 90 MB
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Since the first volume of this work came out in Germany in 1937, this book, together with its first volume, has remained standard in the field. Courant and Hilbert's treatment restores the historically deep connections between physical intuition and mathematical development, providing the reader with a unified approach to mathematical physics. The present volume represents Richard Courant's final revision of 1961.

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