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On The Asymptotic Expansions Of The Confluent Hypergeometric Functions By A Svetlov
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Book Synopsis The Confluent Hypergeometric Function by : Herbert Buchholz
Download or read book The Confluent Hypergeometric Function written by Herbert Buchholz and published by Springer Science & Business Media. This book was released on 2013-11-22 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of this book is the higher transcendental function known as the confluent hypergeometric function. In the last two decades this function has taken on an ever increasing significance because of its use in the application of mathematics to physical and technical problems. There is no doubt that this trend will continue until the general theory of confluent hypergeometric functions becomes familiar to the majority of physicists in much the same way as the cylinder functions, which were previously less well known, are now used in many engineering and physical problems. This book is intended to further this development. The important practical significance of the functions which are treated hardly demands an involved discussion since they include, as special cases, a number of simpler special functions which have long been the everyday tool of the physicist. It is sufficient to mention that these include, among others, the logarithmic integral, the integral sine and cosine, the error integral, the Fresnel integral, the cylinder functions and the cylinder function in parabolic cylindrical coordinates. For anyone who puts forth the effort to study the confluent hypergeometric function in more detail there is the inestimable advantage of being able to understand the properties of other functions derivable from it. This gen eral point of view is particularly useful in connection with series ex pansions valid for values of the argument near zero or infinity and in connection with the various integral representations.
Book Synopsis The Confluent Hypergeometric Function with Special Emphasis on Its Applications by : Herbert Buchholz
Download or read book The Confluent Hypergeometric Function with Special Emphasis on Its Applications written by Herbert Buchholz and published by . This book was released on 1969 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Bulletin of the National Research Council by : National Research Council (U.S.)
Download or read book Bulletin of the National Research Council written by National Research Council (U.S.) and published by . This book was released on 1940 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :National Research Council (U.S.). Committee on a Bibliography on Orthogonal Polynomials Publisher : ISBN 13 : Total Pages :228 pages Book Rating :4.:/5 (89 download)
Book Synopsis A Bibliography on Orthogonal Polynomials by : National Research Council (U.S.). Committee on a Bibliography on Orthogonal Polynomials
Download or read book A Bibliography on Orthogonal Polynomials written by National Research Council (U.S.). Committee on a Bibliography on Orthogonal Polynomials and published by . This book was released on 1940 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Travaux de l'Institut mathématique Stekloff by :
Download or read book Travaux de l'Institut mathématique Stekloff written by and published by . This book was released on 1936 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Bibliography on Continued Fractions, Padé Approximation, Sequence Transformation and Related Subjects by : Claude Brezinski
Download or read book A Bibliography on Continued Fractions, Padé Approximation, Sequence Transformation and Related Subjects written by Claude Brezinski and published by . This book was released on 1991 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Uniform Asymptotic Expansions of Confluent Hypergeometric Functions and Whittaker Functions by : Helge Skovgaard
Download or read book Uniform Asymptotic Expansions of Confluent Hypergeometric Functions and Whittaker Functions written by Helge Skovgaard and published by . This book was released on 1966 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotic Expansions: Their Derivation and Interpretation by : Robert B. Dingle
Download or read book Asymptotic Expansions: Their Derivation and Interpretation written by Robert B. Dingle and published by . This book was released on 1973 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to Asymptotics and Special Functions by : F. W. J. Olver
Download or read book Introduction to Asymptotics and Special Functions written by F. W. J. Olver and published by Academic Press. This book was released on 2014-05-10 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Asymptotics and Special Functions is a comprehensive introduction to two important topics in classical analysis: asymptotics and special functions. The integrals of a real variable are discussed, along with contour integrals and differential equations with regular and irregular singularities. The Liouville-Green approximation is also considered. Comprised of seven chapters, this volume begins with an overview of the basic concepts and definitions of asymptotic analysis and special functions, followed by a discussion on integrals of a real variable. Contour integrals are then examined, paying particular attention to Laplace integrals with a complex parameter and Bessel functions of large argument and order. Subsequent chapters focus on differential equations having regular and irregular singularities, with emphasis on Legendre functions as well as Bessel and confluent hypergeometric functions. A chapter devoted to the Liouville-Green approximation tackles asymptotic properties with respect to parameters and to the independent variable, eigenvalue problems, and theorems on singular integral equations. This monograph is intended for students needing only an introductory course to asymptotics and special functions.
Book Synopsis Asymptotics and Special Functions by : F. W. J. Olver
Download or read book Asymptotics and Special Functions written by F. W. J. Olver and published by Academic Press. This book was released on 2014-05-10 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotics and Special Functions provides a comprehensive introduction to two important topics in classical analysis: asymptotics and special functions. The integrals of a real variable and contour integrals are discussed, along with the Liouville-Green approximation and connection formulas for solutions of differential equations. Differential equations with regular singularities are also considered, with emphasis on hypergeometric and Legendre functions. Comprised of 14 chapters, this volume begins with an introduction to the basic concepts and definitions of asymptotic analysis and special functions, followed by a discussion on asymptotic theories of definite integrals containing a parameter. Contour integrals as well as integrals of a real variable are described. Subsequent chapters deal with the analytic theory of ordinary differential equations; differential equations with regular and irregular singularities; sums and sequences; and connection formulas for solutions of differential equations. The book concludes with an evaluation of methods used in estimating (as opposed to bounding) errors in asymptotic approximations and expansions. This monograph is intended for graduate mathematicians, physicists, and engineers.
Book Synopsis Composite Asymptotic Expansions by : Augustin Fruchard
Download or read book Composite Asymptotic Expansions written by Augustin Fruchard and published by Springer. This book was released on 2012-12-15 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of these lecture notes is to develop a theory of asymptotic expansions for functions involving two variables, while at the same time using functions involving one variable and functions of the quotient of these two variables. Such composite asymptotic expansions (CAsEs) are particularly well-suited to describing solutions of singularly perturbed ordinary differential equations near turning points. CAsEs imply inner and outer expansions near turning points. Thus our approach is closely related to the method of matched asymptotic expansions. CAsEs offer two unique advantages, however. First, they provide uniform expansions near a turning point and away from it. Second, a Gevrey version of CAsEs is available and detailed in the lecture notes. Three problems are presented in which CAsEs are useful. The first application concerns canard solutions near a multiple turning point. The second application concerns so-called non-smooth or angular canard solutions. Finally an Ackerberg-O’Malley resonance problem is solved.
Book Synopsis Asymptotic Expansions by : A. Erdélyi
Download or read book Asymptotic Expansions written by A. Erdélyi and published by Courier Corporation. This book was released on 2012-04-27 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: Various methods for asymptotic evaluation of integrals containing a large parameter, and solutions of ordinary linear differential equations by means of asymptotic expansion.
Book Synopsis Hadamard Expansions and Hyperasymptotic Evaluation by : R. B. Paris
Download or read book Hadamard Expansions and Hyperasymptotic Evaluation written by R. B. Paris and published by Cambridge University Press. This book was released on 2011-03-24 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes a new asymptotic method of high-precision evaluation of certain integrals, related to the classical method of steepest descents.
Book Synopsis Asymptotics and Special Functions by : Frank Olver
Download or read book Asymptotics and Special Functions written by Frank Olver and published by CRC Press. This book was released on 1997-01-24 with total page 591 pages. Available in PDF, EPUB and Kindle. Book excerpt: A classic reference, intended for graduate students mathematicians, physicists, and engineers, this book can be used both as the basis for instructional courses and as a reference tool.
Book Synopsis Asymptotic Expansions by : Johannes Gualtherus Corput
Download or read book Asymptotic Expansions written by Johannes Gualtherus Corput and published by . This book was released on 1951 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotic Expansions for Ordinary Differential Equations by : Wolfgang Wasow
Download or read book Asymptotic Expansions for Ordinary Differential Equations written by Wolfgang Wasow and published by Courier Dover Publications. This book was released on 2018-03-21 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: This outstanding text concentrates on the mathematical ideas underlying various asymptotic methods for ordinary differential equations that lead to full, infinite expansions. "A book of great value." — Mathematical Reviews. 1976 revised edition.
Book Synopsis Asymptotic Expansions by : Edward Thomas Copson
Download or read book Asymptotic Expansions written by Edward Thomas Copson and published by Cambridge University Press. This book was released on 1965-01-01 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic representation of a function os of great importance in many branches of pure and applied mathematics.
