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Further Rational Approximations For The Incomplete Gamma Functions
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Book Synopsis Further Rational Approximations for the Incomplete Gamma Functions by : Midwest Research Institute (Kansas City, Mo.)
Download or read book Further Rational Approximations for the Incomplete Gamma Functions written by Midwest Research Institute (Kansas City, Mo.) and published by . This book was released on 1963 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Further Rational Approximations for the Incomplete Gamma Function by : Yudell L. Luke
Download or read book Further Rational Approximations for the Incomplete Gamma Function written by Yudell L. Luke and published by . This book was released on 1963 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a previous report we studied rational approximations to the incomplete gamma function. These were based on the asymptotic expansion of the latter function. In the present study, a similar analysis is done for the same function based on one of its ascending series representations. The work is related to other developments, but there are numerous improvements and some new features.
Book Synopsis Rational Approximations for the Incomplete Gamma Function by : Midwest Research Institute (Kansas City, Mo.)
Download or read book Rational Approximations for the Incomplete Gamma Function written by Midwest Research Institute (Kansas City, Mo.) and published by . This book was released on 1962 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1992 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Special Functions and Their Approximations: v. 2 by : Yudell L. Luke
Download or read book Special Functions and Their Approximations: v. 2 written by Yudell L. Luke and published by Academic Press. This book was released on 1969 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: Special Functions and Their Approximations: v. 2
Book Synopsis Algorithms for Rational Approximations for a Confluent Hypergeometric Function by : Yudell L. Lake
Download or read book Algorithms for Rational Approximations for a Confluent Hypergeometric Function written by Yudell L. Lake and published by . This book was released on 1976 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the authors' volumes on the special functions, rational approximations for the confluent hypergeometric function (z sup a)U(a;c;z) were examined in some detail. This confluent function is very important in the applications since it includes as special cases the incomplete gamma function (special cases of which are exponential, sine and cosine integrals, Fresnel integrals and the error function), Bessel functions, parabolic cylinder functions and Coulomb wave functions. In the special case where a is unity, the confluent function becomes an incomplete gamma function. In this event, complete a priori error analyses for the main diagonal Pade approximations and much more were presented. For general parameters, the rational approximations treated were not of the Pade class. It was shown that the rational approximations converge, but a complete a priori analysis was not available. One of the purposes of this report is to correct this deficiency. FORTRAN programs are provided to evaluate the Pade and non-Pade rational approximations by using the appropriate recursion formulas to generate the numerator and denominator polynomials as a number, and to also evaluate the coefficients which define these polynomials.
Book Synopsis On a Class of Incomplete Gamma Functions with Applications by : M. Aslam Chaudhry
Download or read book On a Class of Incomplete Gamma Functions with Applications written by M. Aslam Chaudhry and published by CRC Press. This book was released on 2001-08-21 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of special functions is rich and expanding continuously with the emergence of new problems encountered in engineering and applied science applications. The development of computational techniques and the rapid growth in computing power have increased the importance of the special functions and their formulae for analytic representations
Book Synopsis Approximation of the Incomplete Gamma Function, [subscript] X↑2-tests by : Triumf
Download or read book Approximation of the Incomplete Gamma Function, [subscript] X↑2-tests written by Triumf and published by . This book was released on 1992 with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Algorithms for Rational Approximations for a Confluent Hypergeometric Function II. by : Yudell L. Luke
Download or read book Algorithms for Rational Approximations for a Confluent Hypergeometric Function II. written by Yudell L. Luke and published by . This book was released on 1976 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a sequel to a previous paper where rational approximations for the confluent hypergeometric function were treated. Here we take up rational approximations for (1)F(1)(a;c;-z). The confluent functions are very important in the applications since they include as special cases the incomplete gamma function Bessel functions, parabolic cylinder functions and Coulomb wave functions. In the special case where a is unity, the confluent function becomes an incomplete gamma function. In this event, complete a priori error analyses for the main diagonal Pade approximations and much more were presented. For general parameters, the rational approximations treated were not of the Pade class. It was shown that the rational approximations converge, but a complete a priori analysis was not available. One of the purposes of this report is to correct this deficiency.
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1963 with total page 1196 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis U.S. Government Research Reports by :
Download or read book U.S. Government Research Reports written by and published by . This book was released on 1964 with total page 1310 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Pade and Rational Approximation by : E.B. Safe
Download or read book Pade and Rational Approximation written by E.B. Safe and published by Elsevier. This book was released on 2013-05-09 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: Padé and Rational Approximation: Theory and Applications presents the proceedings of the Conference on Rational Approximation with Emphasis on Applications of Padé Approximants, held in Tampa, Florida on December 15-17, 1976. The contributors focus on the interplay of theory, computation, and physical applications. This book is composed of six parts encompassing 44 chapters. The introductory part discusses the general theory of orthogonal polynomials that is the mathematical basis of Padé approximants and related matters evaluation. This text also examines the connection between approximants on a stepline in the ordinary Padé table and certain continued fractions and the convergence of diagonal Padé approximants to a class of functions with an even number of branch points. The following parts deal with the special functions and continued fractions of Padé approximation and the theory of rational approximations. These parts also investigate the geometric convergence of Chebyshev rational approximation on the half line, the optimal approximation by “Almost Classical interpolation, and the incomplete polynomials approximation. The discussion then shifts to the physical applications and computations of the Padé approximants. The concluding part presents the applications of rational approximation to gun fire control and to the White Sands Missile Range Computer Facility. This part also provides a list of some open problems and conjectures concerning polynomials and rational functions. This book is of great benefit to mathematicians, physicists, and laboratory workers.
Book Synopsis Numerical Methods for Special Functions by : Amparo Gil
Download or read book Numerical Methods for Special Functions written by Amparo Gil and published by SIAM. This book was released on 2007-01-01 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: An overview that advises when to use specific methods depending upon the function and range.
Book Synopsis Government reports annual index by :
Download or read book Government reports annual index written by and published by . This book was released on 199? with total page 1314 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Extrapolation and Rational Approximation by : Claude Brezinski
Download or read book Extrapolation and Rational Approximation written by Claude Brezinski and published by Springer Nature. This book was released on 2020-11-30 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book paints a fresco of the field of extrapolation and rational approximation over the last several centuries to the present through the works of their primary contributors. It can serve as an introduction to the topics covered, including extrapolation methods, Padé approximation, orthogonal polynomials, continued fractions, Lanczos-type methods etc.; it also provides in depth discussion of the many links between these subjects. A highlight of this book is the presentation of the human side of the fields discussed via personal testimonies from contemporary researchers, their anecdotes, and their exclusive remembrances of some of the “actors.” This book shows how research in this domain started and evolved. Biographies of other scholars encountered have also been included. An important branch of mathematics is described in its historical context, opening the way to new developments. After a mathematical introduction, the book contains a precise description of the mathematical landscape of these fields spanning from the 19th century to the first part of the 20th. After an analysis of the works produced after that period (in particular those of Richardson, Aitken, Shanks, Wynn, and others), the most recent developments and applications are reviewed.
Book Synopsis Continued Fractions: From Analytic Number Theory to Constructive Approximation by : Bruce C. Berndt
Download or read book Continued Fractions: From Analytic Number Theory to Constructive Approximation written by Bruce C. Berndt and published by American Mathematical Soc.. This book was released on 1999 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the contributions from the international conference held at the University of Missouri at Columbia, marking Professor Lange's 70th birthday and his retirement from the university. The principal purpose of the conference was to focus on continued fractions as a common interdisciplinary theme bridging gaps between a large number of fields-from pure mathematics to mathematical physics and approximation theory. Evident in this work is the widespread influence of continued fractions in a broad range of areas of mathematics and physics, including number theory, elliptic functions, Padé approximations, orthogonal polynomials, moment problems, frequency analysis, and regularity properties of evolution equations. Different areas of current research are represented. The lectures at the conference and the contributions to this volume reflect the wide range of applicability of continued fractions in mathematics and the applied sciences.
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