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Mathematical Functions and Their Approximations

Author: Yudell L. Luke

Publisher: Academic Press

Published: 2014-05-10

Total Pages: 587

ISBN-13: 1483262456

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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.

Book Synopsis Mathematical Functions and Their Approximations by : Yudell L. Luke

Download or read book Mathematical Functions and Their Approximations written by Yudell L. Luke and published by Academic Press. This book was released on 2014-05-10 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author: Yudell L. Luke

Publisher: Academic Press

Published: 1969

Total Pages: 348

ISBN-13: 0080955606

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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.

Book Synopsis The Special Functions and Their Approximations by : Yudell L. Luke

Download or read book The Special Functions and Their Approximations written by Yudell L. Luke and published by Academic Press. This book was released on 1969 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematical Functions and Their Approximations

Author: Yudell L. Luke

Publisher:

Published: 1964

Total Pages: 0

ISBN-13:

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Book Synopsis Mathematical Functions and Their Approximations by : Yudell L. Luke

Download or read book Mathematical Functions and Their Approximations written by Yudell L. Luke and published by . This book was released on 1964 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

An Introduction to the Approximation of Functions

Author: Theodore J. Rivlin

Publisher: Courier Corporation

Published: 1981-01-01

Total Pages: 164

ISBN-13: 9780486640693

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Mathematics of Computing -- Numerical Analysis.

Book Synopsis An Introduction to the Approximation of Functions by : Theodore J. Rivlin

Download or read book An Introduction to the Approximation of Functions written by Theodore J. Rivlin and published by Courier Corporation. This book was released on 1981-01-01 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.

Handbook of Mathematical Functions

Author: Milton Abramowitz

Publisher: Courier Corporation

Published: 1965-01-01

Total Pages: 1068

ISBN-13: 9780486612720

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

Book Synopsis Handbook of Mathematical Functions by : Milton Abramowitz

Download or read book Handbook of Mathematical Functions written by Milton Abramowitz and published by Courier Corporation. This book was released on 1965-01-01 with total page 1068 pages. Available in PDF, EPUB and Kindle. Book excerpt: An extensive summary of mathematical functions that occur in physical and engineering problems

Special Functions and Their Approximations:

Author: Yudell L. Luke

Publisher: Academic Press

Published: 1969

Total Pages: 484

ISBN-13: 0080955614

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Special Functions and Their Approximations: v. 2

Book Synopsis Special Functions and Their Approximations: by : Yudell L. Luke

Download or read book Special Functions and Their Approximations: written by Yudell L. Luke and published by Academic Press. This book was released on 1969 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: Special Functions and Their Approximations: v. 2

Mathematical Functions and Their Approximations. an Updated Version of Part of Handbook of Mathematical Functions

Author: YUDELL L. LUKE

Publisher:

Published: 1975

Total Pages: 568

ISBN-13:

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Book Synopsis Mathematical Functions and Their Approximations. an Updated Version of Part of Handbook of Mathematical Functions by : YUDELL L. LUKE

Download or read book Mathematical Functions and Their Approximations. an Updated Version of Part of Handbook of Mathematical Functions written by YUDELL L. LUKE and published by . This book was released on 1975 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Approximation Theory and Methods

Author: M. J. D. Powell

Publisher: Cambridge University Press

Published: 1981-03-31

Total Pages: 356

ISBN-13: 9780521295147

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Most functions that occur in mathematics cannot be used directly in computer calculations. Instead they are approximated by manageable functions such as polynomials and piecewise polynomials. The general theory of the subject and its application to polynomial approximation are classical, but piecewise polynomials have become far more useful during the last twenty years. Thus many important theoretical properties have been found recently and many new techniques for the automatic calculation of approximations to prescribed accuracy have been developed. This book gives a thorough and coherent introduction to the theory that is the basis of current approximation methods. Professor Powell describes and analyses the main techniques of calculation supplying sufficient motivation throughout the book to make it accessible to scientists and engineers who require approximation methods for practical needs. Because the book is based on a course of lectures to third-year undergraduates in mathematics at Cambridge University, sufficient attention is given to theory to make it highly suitable as a mathematical textbook at undergraduate or postgraduate level.

Book Synopsis Approximation Theory and Methods by : M. J. D. Powell

Download or read book Approximation Theory and Methods written by M. J. D. Powell and published by Cambridge University Press. This book was released on 1981-03-31 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most functions that occur in mathematics cannot be used directly in computer calculations. Instead they are approximated by manageable functions such as polynomials and piecewise polynomials. The general theory of the subject and its application to polynomial approximation are classical, but piecewise polynomials have become far more useful during the last twenty years. Thus many important theoretical properties have been found recently and many new techniques for the automatic calculation of approximations to prescribed accuracy have been developed. This book gives a thorough and coherent introduction to the theory that is the basis of current approximation methods. Professor Powell describes and analyses the main techniques of calculation supplying sufficient motivation throughout the book to make it accessible to scientists and engineers who require approximation methods for practical needs. Because the book is based on a course of lectures to third-year undergraduates in mathematics at Cambridge University, sufficient attention is given to theory to make it highly suitable as a mathematical textbook at undergraduate or postgraduate level.

Mathematics of Approximation

Author: Johan De Villiers

Publisher: Springer Science & Business Media

Published: 2012-06-30

Total Pages: 418

ISBN-13: 9491216503

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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

Book Synopsis Mathematics of Approximation by : Johan De Villiers

Download or read book Mathematics of Approximation written by Johan De Villiers and published by Springer Science & Business Media. This book was released on 2012-06-30 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Analytic Number Theory, Approximation Theory, and Special Functions

Author: Gradimir V. Milovanović

Publisher: Springer

Published: 2014-07-08

Total Pages: 873

ISBN-13: 149390258X

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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.

Book Synopsis Analytic Number Theory, Approximation Theory, and Special Functions by : Gradimir V. Milovanović

Download or read book Analytic Number Theory, Approximation Theory, and Special Functions written by Gradimir V. Milovanović and published by Springer. This book was released on 2014-07-08 with total page 873 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.