Computation Of Special Functions PDF Download

Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Computation Of Special Functions PDF full book. Access full book title Computation Of Special Functions.

Computation of Special Functions

Computation of Special Functions
Author: Shanjie Zhang
Publisher: Wiley-Interscience
Total Pages: 752
Release: 1996-07-26
Genre: Computers
ISBN:

Download Computation of Special Functions Book in PDF, ePub and Kindle

Computation of Special Functions is a valuable book/software package containing more than 100 original computer programs for the computation of most special functions currently in use. These include many functions commonly omitted from available software packages, such as the Bessel and modified Bessel functions, the Mathieu and modified Mathieu functions, parabolic cylinder functions, and various prolate and oblate spheroidal wave functions. Also, unlike most software packages, this book/disk set gives readers the latitude to modify programs according to the special demands of the sophisticated problems they are working on. The authors provide detailed descriptions of the program's algorithms as well as specific information about each program's internal structure.


Special Functions in Physics with MATLAB

Special Functions in Physics with MATLAB
Author: Wolfgang Schweizer
Publisher: Springer Nature
Total Pages: 282
Release: 2021-03-25
Genre: Science
ISBN: 3030642321

Download Special Functions in Physics with MATLAB Book in PDF, ePub and Kindle

This handbook focuses on special functions in physics in the real and complex domain. It covers more than 170 different functions with additional numerical hints for efficient computation, which are useful to anyone who needs to program with other programming languages as well. The book comes with MATLAB-based programs for each of these functions and a detailed html-based documentation. Some of the explained functions are: Gamma and Beta functions; Legendre functions, which are linked to quantum mechanics and electrodynamics; Bessel functions; hypergeometric functions, which play an important role in mathematical physics; orthogonal polynomials, which are largely used in computational physics; and Riemann zeta functions, which play an important role, e.g., in quantum chaos or string theory. The book’s primary audience are scientists, professionals working in research areas of industries, and advanced students in physics, applied mathematics, and engineering.


Numerical Methods for Special Functions

Numerical Methods for Special Functions
Author: Amparo Gil
Publisher: SIAM
Total Pages: 431
Release: 2007-01-01
Genre: Mathematics
ISBN: 9780898717822

Download Numerical Methods for Special Functions Book in PDF, ePub and Kindle

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).


Formulas and Theorems for the Special Functions of Mathematical Physics

Formulas and Theorems for the Special Functions of Mathematical Physics
Author: Wilhelm Magnus
Publisher: Springer Science & Business Media
Total Pages: 516
Release: 2013-11-11
Genre: Science
ISBN: 3662117614

Download Formulas and Theorems for the Special Functions of Mathematical Physics Book in PDF, ePub and Kindle

This is a new and enlarged English edition of the book which, under the title "Formeln und Satze fur die Speziellen Funktionen der mathe matischen Physik" appeared in German in 1946. Much of the material (part of it unpublished) did not appear in the earlier editions. We hope that these additions will be useful and yet not too numerous for the purpose of locating .with ease any particular result. Compared to the first two (German) editions a change has taken place as far as the list of references is concerned. They are generally restricted to books and monographs and accomodated at the end of each individual chapter. Occasional references to papers follow those results to which they apply. The authors felt a certain justification for this change. At the time of the appearance of the previous edition nearly twenty years ago much of the material was scattered over a number of single contributions. Since then most of it has been included in books and monographs with quite exhaustive bibliographies. For information about numerical tables the reader is referred to "Mathematics of Computation", a periodical publis hed by the American Mathematical Society; "Handbook of Mathe matical Functions" with formulas, graphs and mathematical tables National Bureau of Standards Applied Mathematics Series, 55, 1964, 1046 pp., Government Printing Office, Washington, D.C., and FLETCHER, MILLER, ROSENHEAD, Index of Mathematical Tables, Addison-Wesley, Reading, Mass.) .. There is a list of symbols and abbreviations at the end of the book.


Orthogonal Polynomials and Special Functions

Orthogonal Polynomials and Special Functions
Author: Francisco Marcellàn
Publisher: Springer Science & Business Media
Total Pages: 432
Release: 2006-06-19
Genre: Mathematics
ISBN: 3540310622

Download Orthogonal Polynomials and Special Functions Book in PDF, ePub and Kindle

Special functions and orthogonal polynomials in particular have been around for centuries. Can you imagine mathematics without trigonometric functions, the exponential function or polynomials? In the twentieth century the emphasis was on special functions satisfying linear differential equations, but this has now been extended to difference equations, partial differential equations and non-linear differential equations. The present set of lecture notes containes seven chapters about the current state of orthogonal polynomials and special functions and gives a view on open problems and future directions. The topics are: computational methods and software for quadrature and approximation, equilibrium problems in logarithmic potential theory, discrete orthogonal polynomials and convergence of Krylov subspace methods in numerical linear algebra, orthogonal rational functions and matrix orthogonal rational functions, orthogonal polynomials in several variables (Jack polynomials) and separation of variables, a classification of finite families of orthogonal polynomials in Askey’s scheme using Leonard pairs, and non-linear special functions associated with the Painlevé equations.


The Mathematical-Function Computation Handbook

The Mathematical-Function Computation Handbook
Author: Nelson H.F. Beebe
Publisher: Springer
Total Pages: 1145
Release: 2017-08-20
Genre: Computers
ISBN: 3319641107

Download The Mathematical-Function Computation Handbook Book in PDF, ePub and Kindle

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.


Special Functions

Special Functions
Author: George E. Andrews
Publisher: Cambridge University Press
Total Pages: 684
Release: 1999
Genre: Mathematics
ISBN: 9780521789882

Download Special Functions Book in PDF, ePub and Kindle

An overview of special functions, focusing on the hypergeometric functions and the associated hypergeometric series.


Handbook of Mathematical Functions

Handbook of Mathematical Functions
Author: Milton Abramowitz
Publisher: Courier Corporation
Total Pages: 1068
Release: 1965-01-01
Genre: Mathematics
ISBN: 9780486612720

Download Handbook of Mathematical Functions Book in PDF, ePub and Kindle

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


Riemann-Hilbert Problems, Their Numerical Solution, and the Computation of Nonlinear Special Functions

Riemann-Hilbert Problems, Their Numerical Solution, and the Computation of Nonlinear Special Functions
Author: Thomas Trogdon
Publisher: SIAM
Total Pages: 370
Release: 2015-12-22
Genre: Mathematics
ISBN: 1611974208

Download Riemann-Hilbert Problems, Their Numerical Solution, and the Computation of Nonlinear Special Functions Book in PDF, ePub and Kindle

Riemann?Hilbert problems are fundamental objects of study within complex analysis. Many problems in differential equations and integrable systems, probability and random matrix theory, and asymptotic analysis can be solved by reformulation as a Riemann?Hilbert problem.This book, the most comprehensive one to date on the applied and computational theory of Riemann?Hilbert problems, includes an introduction to computational complex analysis, an introduction to the applied theory of Riemann?Hilbert problems from an analytical and numerical perspective, and a discussion of applications to integrable systems, differential equations, and special function theory. It also includes six fundamental examples and five more sophisticated examples of the analytical and numerical Riemann?Hilbert method, each of mathematical or physical significance or both.


Handbook of Continued Fractions for Special Functions

Handbook of Continued Fractions for Special Functions
Author: Annie A.M. Cuyt
Publisher: Springer Science & Business Media
Total Pages: 430
Release: 2008-04-12
Genre: Mathematics
ISBN: 1402069499

Download Handbook of Continued Fractions for Special Functions Book in PDF, ePub and Kindle

Special functions are pervasive in all fields of science and industry. The most well-known application areas are in physics, engineering, chemistry, computer science and statistics. Because of their importance, several books and websites (see for instance http: functions.wolfram.com) and a large collection of papers have been devoted to these functions. Of the standard work on the subject, the Handbook of mathematical functions with formulas, graphs and mathematical tables edited by Milton Abramowitz and Irene Stegun, the American National Institute of Standards claims to have sold over 700 000 copies! But so far no project has been devoted to the systematic study of continued fraction representations for these functions. This handbook is the result of such an endeavour. We emphasise that only 10% of the continued fractions contained in this book, can also be found in the Abramowitz and Stegun project or at the Wolfram website!