The Special Functions and Their Approximations

The Special Functions and Their Approximations PDF

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.

Mathematical Functions and Their Approximations

Mathematical Functions and Their Approximations PDF

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.

Analytic Number Theory, Approximation Theory, and Special Functions

Analytic Number Theory, Approximation Theory, and Special Functions PDF

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.

Numerical Methods for Special Functions

Numerical Methods for Special Functions PDF

Author: Amparo Gil

Publisher: SIAM

Published: 2007-01-01

Total Pages: 431

ISBN-13: 9780898717822

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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).

Handbook of Mathematical Functions

Handbook of Mathematical Functions PDF

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

Theory and Applications of Special Functions

Theory and Applications of Special Functions PDF

Author: Mourad E. H. Ismail

Publisher: Springer Science & Business Media

Published: 2006-03-30

Total Pages: 497

ISBN-13: 0387242333

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A collection of articles on various aspects of q-series and special functions dedicated to Mizan Rahman. It also includes an article by Askey, Ismail, and Koelink on Rahman’s mathematical contributions and how they influenced the recent upsurge in the subject.

Special Functions

Special Functions PDF

Author: Nico M. Temme

Publisher: John Wiley & Sons

Published: 1996-02-22

Total Pages: 398

ISBN-13: 9780471113133

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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.

Bessel Functions and Their Applications

Bessel Functions and Their Applications PDF

Author: B G Korenev

Publisher: CRC Press

Published: 2002-07-25

Total Pages: 290

ISBN-13: 9780203216927

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Bessel functions are associated with a wide range of problems in important areas of mathematical physics. Bessel function theory is applied to problems of acoustics, radio physics, hydrodynamics, and atomic and nuclear physics. Bessel Functions and Their Applications consists of two parts. In Part One, the author presents a clear and rigorous intro

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