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Author: Yudell L. Luke
Publisher: Academic Press
ISBN: 1483262456
Category : Mathematics
Languages : en
Pages : 587
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Book Description
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
ISBN: 1483262456
Category : Mathematics
Languages : en
Pages : 587
Get Book Here
Book Description
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
ISBN: 0080955606
Category : Mathematics
Languages : en
Pages : 373
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Book Description
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:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Theodore J. Rivlin
Publisher: Courier Corporation
ISBN: 9780486640693
Category : Mathematics
Languages : en
Pages : 164
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Book Description
Mathematics of Computing -- Numerical Analysis.
Author: Milton Abramowitz
Publisher: Courier Corporation
ISBN: 9780486612720
Category : Mathematics
Languages : en
Pages : 1068
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Book Description
An extensive summary of mathematical functions that occur in physical and engineering problems
Author: Yudell L. Luke
Publisher: Academic Press
ISBN: 0080955614
Category : Computers
Languages : en
Pages : 509
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Book Description
Special Functions and Their Approximations: v. 2
Author: Amparo Gil
Publisher: SIAM
ISBN: 9780898717822
Category : Mathematics
Languages : en
Pages : 431
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Book Description
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: Gradimir V. Milovanović
Publisher: Springer
ISBN: 149390258X
Category : Mathematics
Languages : en
Pages : 873
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Book Description
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: A. F. Timan
Publisher: Elsevier
ISBN: 1483184811
Category : Mathematics
Languages : en
Pages : 644
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Book Description
Theory of Approximation of Functions of a Real Variable discusses a number of fundamental parts of the modern theory of approximation of functions of a real variable. The material is grouped around the problem of the connection between the best approximation of functions to their structural properties. This text is composed of eight chapters that highlight the relationship between the various structural properties of real functions and the character of possible approximations to them by polynomials and other functions of simple construction. Each chapter concludes with a section containing various problems and theorems, which supplement the main text. The first chapters tackle the Weierstrass's theorem, the best approximation by polynomials on a finite segment, and some compact classes of functions and their structural properties. The subsequent chapters describe some properties of algebraic polynomials and transcendental integral functions of exponential type, as well as the direct theorems of the constructive theory of functions. These topics are followed by discussions of differential and constructive characteristics of converse theorems. The final chapters explore other theorems connecting the best approximations functions with their structural properties. These chapters also deal with the linear processes of approximation of functions by polynomials. The book is intended for post-graduate students and for mathematical students taking advanced courses, as well as to workers in the field of the theory of functions.
Author: Lloyd N. Trefethen
Publisher: SIAM
ISBN: 1611975948
Category : Mathematics
Languages : en
Pages : 377
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Book Description
This is a textbook on classical polynomial and rational approximation theory for the twenty-first century. Aimed at advanced undergraduates and graduate students across all of applied mathematics, it uses MATLAB to teach the fields most important ideas and results. Approximation Theory and Approximation Practice, Extended Edition differs fundamentally from other works on approximation theory in a number of ways: its emphasis is on topics close to numerical algorithms; concepts are illustrated with Chebfun; and each chapter is a PUBLISHable MATLAB M-file, available online. The book centers on theorems and methods for analytic functions, which appear so often in applications, rather than on functions at the edge of discontinuity with their seductive theoretical challenges. Original sources are cited rather than textbooks, and each item in the bibliography is accompanied by an editorial comment. In addition, each chapter has a collection of exercises, which span a wide range from mathematical theory to Chebfun-based numerical experimentation. This textbook is appropriate for advanced undergraduate or graduate students who have an understanding of numerical analysis and complex analysis. It is also appropriate for seasoned mathematicians who use MATLAB.
