The Special Functions And Their Approximations

Author : Yudell L. Luke
Publisher : Academic Press
Page : 348 pages
File Size : 50,9 Mb
Release : 1969
Category : Mathematics
ISBN : 9780080955605

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The Special Functions and Their Approximations by Yudell L. Luke Pdf

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.

Author : Yudell L. Luke
Publisher : Academic Press
Page : 587 pages
File Size : 43,7 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483262451

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Mathematical Functions and Their Approximations by Yudell L. Luke Pdf

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.

Author : Yudell L. Luke
Publisher : Academic Press
Page : 484 pages
File Size : 46,7 Mb
Release : 1969
Category : Computers
ISBN : 9780080955612

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Special Functions and Their Approximations: by Yudell L. Luke Pdf

Special Functions and Their Approximations: v. 2

Author : Gradimir V. Milovanović,Michael Th. Rassias
Publisher : Springer
Page : 873 pages
File Size : 45,6 Mb
Release : 2014-07-08
Category : Mathematics
ISBN : 9781493902583

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Analytic Number Theory, Approximation Theory, and Special Functions by Gradimir V. Milovanović,Michael Th. Rassias Pdf

This book, in honor of Hari M. Srivastava, discusses essential developments in mathematical research in a variety of problems. It contains thirty-five articles, written by eminent scientists from the international mathematical community, including both research and survey works. Subjects covered include analytic number theory, combinatorics, special sequences of numbers and polynomials, analytic inequalities and applications, approximation of functions and quadratures, orthogonality and special and complex functions. The mathematical results and open problems discussed in this book are presented in a simple and self-contained manner. The book contains an overview of old and new results, methods, and theories toward the solution of longstanding problems in a wide scientific field, as well as new results in rapidly progressing areas of research. The book will be useful for researchers and graduate students in the fields of mathematics, physics and other computational and applied sciences.

Author : Milton Abramowitz,Irene A. Stegun
Publisher : Courier Corporation
Page : 1068 pages
File Size : 55,5 Mb
Release : 1965-01-01
Category : Mathematics
ISBN : 0486612724

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Handbook of Mathematical Functions by Milton Abramowitz,Irene A. Stegun Pdf

An extensive summary of mathematical functions that occur in physical and engineering problems

Author : Amparo Gil,Javier Segura,Nico M. Temme
Publisher : SIAM
Page : 431 pages
File Size : 45,9 Mb
Release : 2007-01-01
Category : Mathematics
ISBN : 0898717825

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Numerical Methods for Special Functions by Amparo Gil,Javier Segura,Nico M. Temme Pdf

Special functions arise in many problems of pure and applied mathematics, mathematical statistics, physics, and engineering. This book provides an up-to-date overview of numerical methods for computing special functions and discusses when to use these methods depending on the function and the range of parameters. Not only are standard and simple parameter domains considered, but methods valid for large and complex parameters are described as well. The first part of the book (basic methods) covers convergent and divergent series, Chebyshev expansions, numerical quadrature, and recurrence relations. Its focus is on the computation of special functions; however, it is suitable for general numerical courses. Pseudoalgorithms are given to help students write their own algorithms. In addition to these basic tools, the authors discuss other useful and efficient methods, such as methods for computing zeros of special functions, uniform asymptotic expansions, Padé approximations, and sequence transformations. The book also provides specific algorithms for computing several special functions (like Airy functions and parabolic cylinder functions, among others).

Author : Theodore J. Rivlin
Publisher : Courier Corporation
Page : 164 pages
File Size : 46,5 Mb
Release : 1981-01-01
Category : Mathematics
ISBN : 0486640698

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An Introduction to the Approximation of Functions by Theodore J. Rivlin Pdf

Mathematics of Computing -- Numerical Analysis.

Author : Richard Askey
Publisher : Academic Press
Page : 573 pages
File Size : 54,5 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483216164

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Theory and Application of Special Functions by Richard Askey Pdf

Theory and Application of Special Functions contains the proceedings of the Advanced Seminar on Special Functions sponsored by the Mathematics Research Center of the University of Wisconsin-Madison and held from March 31 to April 2, 1975. The seminar tackled the theory and application of special functions and covered topics ranging from the asymptotic estimation of special functions to association schemes and coding theory. Some interesting results, conjectures, and problems are given. Comprised of 13 chapters, this book begins with a survey of computational methods in special functions, followed by a discussion on unsolved problems in the asymptotic estimation of special functions. The reader is then introduced to periodic Bernoulli numbers, summation formulas, and applications; problems and prospects for basic hypergeometric functions; and linear growth models with many types and multidimensional Hahn polynomials. Subsequent chapters explore two-variable analogues of the classical orthogonal polynomials; special functions of matrix and single argument in statistics; and some properties of the determinants of orthogonal polynomials. This monograph is intended primarily for students and practitioners of mathematics.

Author : Nico M. Temme
Publisher : John Wiley & Sons
Page : 398 pages
File Size : 43,5 Mb
Release : 1996-02-22
Category : Mathematics
ISBN : 0471113131

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Special Functions by Nico M. Temme Pdf

This book gives an introduction to the classical, well-known special functions which play a role in mathematical physics, especially in boundary value problems. Calculus and complex function theory form the basis of the book and numerous formulas are given. Particular attention is given to asymptomatic and numerical aspects of special functions, with numerous references to recent literature provided.

Author : Z. X. Wang,D. R. Guo
Publisher : World Scientific
Page : 720 pages
File Size : 52,9 Mb
Release : 1989
Category : Mathematics
ISBN : 997150667X

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Special Functions by Z. X. Wang,D. R. Guo Pdf

Contains the various principal special functions in common use and their basic properties and manipulations. Discusses expansions of functions in infinite series and infinite product and the asymptotic expansion of functions. For physicists, engineers, and mathematicians. Acidic paper. Paper edition (unseen), $38. Annotation copyrighted by Book News, Inc., Portland, OR

Author : C. G. van der Laan,N. M. Temme
Publisher : Unknown
Page : 250 pages
File Size : 41,8 Mb
Release : 1984
Category : Error functions
ISBN : UOM:39015015698627

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Calculation of Special Functions by C. G. van der Laan,N. M. Temme Pdf

Author : N. N. Lebedev
Publisher : Courier Corporation
Page : 340 pages
File Size : 49,9 Mb
Release : 2012-04-30
Category : Mathematics
ISBN : 9780486139890

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Special Functions & Their Applications by N. N. Lebedev Pdf

Famous Russian work discusses the application of cylinder functions and spherical harmonics; gamma function; probability integral and related functions; Airy functions; hyper-geometric functions; more. Translated by Richard Silverman.

Author : F. W. J. Olver
Publisher : Academic Press
Page : 589 pages
File Size : 41,7 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483267449

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Asymptotics and Special Functions by F. W. J. Olver Pdf

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.

Author : Clifford Truesdell
Publisher : Princeton University Press
Page : 200 pages
File Size : 48,7 Mb
Release : 1949-01-20
Category : Mathematics
ISBN : 0691095779

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An Essay Toward a Unified Theory of Special Functions by Clifford Truesdell Pdf

The description for this book, An Essay Toward a Unified Theory of Special Functions. (AM-18), Volume 18, will be forthcoming.

Author : Frank W. J. Olver
Publisher : Cambridge University Press
Page : 968 pages
File Size : 55,9 Mb
Release : 2010-05-17
Category : Mathematics
ISBN : 9780521192255

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NIST Handbook of Mathematical Functions Hardback and CD-ROM by Frank W. J. Olver Pdf

The new standard reference on mathematical functions, replacing the classic but outdated handbook from Abramowitz and Stegun. Includes PDF version.