Mathematical Functions And Their Approximations
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Author | : Yudell L. Luke |
Publisher | : Academic Press |
Total Pages | : 587 |
Release | : 2014-05-10 |
Genre | : Mathematics |
ISBN | : 1483262456 |
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 |
Total Pages | : 373 |
Release | : 1969 |
Genre | : Mathematics |
ISBN | : 0080955606 |
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 | : |
Total Pages | : 0 |
Release | : 1964 |
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Author | : Yudell L. Luke |
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Author | : YUDELL L. LUKE |
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Total Pages | : 568 |
Release | : 1975 |
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Author | : Yudell L. Luke |
Publisher | : Academic Press |
Total Pages | : 509 |
Release | : 1969 |
Genre | : Computers |
ISBN | : 0080955614 |
Special Functions and Their Approximations: v. 2
Author | : Milton Abramowitz |
Publisher | : Courier Corporation |
Total Pages | : 1068 |
Release | : 1965-01-01 |
Genre | : Mathematics |
ISBN | : 9780486612720 |
An extensive summary of mathematical functions that occur in physical and engineering problems
Author | : Frank W. J. Olver |
Publisher | : Cambridge University Press |
Total Pages | : 968 |
Release | : 2010-05-17 |
Genre | : Mathematics |
ISBN | : 0521192250 |
The new standard reference on mathematical functions, replacing the classic but outdated handbook from Abramowitz and Stegun. Includes PDF version.
Author | : A. F. Timan |
Publisher | : Elsevier |
Total Pages | : 644 |
Release | : 2014-07-22 |
Genre | : Mathematics |
ISBN | : 1483184811 |
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 | : Nelson H.F. Beebe |
Publisher | : Springer |
Total Pages | : 1145 |
Release | : 2017-08-20 |
Genre | : Computers |
ISBN | : 3319641107 |
This highly comprehensive handbook provides a substantial advance in the computation of elementary and special functions of mathematics, extending the function coverage of major programming languages well beyond their international standards, including full support for decimal floating-point arithmetic. Written with clarity and focusing on the C language, the work pays extensive attention to little-understood aspects of floating-point and integer arithmetic, and to software portability, as well as to important historical architectures. It extends support to a future 256-bit, floating-point format offering 70 decimal digits of precision. Select Topics and Features: references an exceptionally useful, author-maintained MathCW website, containing source code for the book’s software, compiled libraries for numerous systems, pre-built C compilers, and other related materials; offers a unique approach to covering mathematical-function computation using decimal arithmetic; provides extremely versatile appendices for interfaces to numerous other languages: Ada, C#, C++, Fortran, Java, and Pascal; presupposes only basic familiarity with computer programming in a common language, as well as early level algebra; supplies a library that readily adapts for existing scripting languages, with minimal effort; supports both binary and decimal arithmetic, in up to 10 different floating-point formats; covers a significant portion (with highly accurate implementations) of the U.S National Institute of Standards and Technology’s 10-year project to codify mathematical functions. This highly practical text/reference is an invaluable tool for advanced undergraduates, recording many lessons of the intermingled history of computer hardw are and software, numerical algorithms, and mathematics. In addition, professional numerical analysts and others will find the handbook of real interest and utility because it builds on research by the mathematical software community over the last four decades.