Uniform Asymptotic Expansions of Confluent Hypergeometric Functions and Whittaker Functions
Author: Helge Skovgaard
Publisher:
Published: 1966
Total Pages: 104
ISBN-13:
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Asymptotic Forms of Whittaker's Confluent Hypergeometric Functions
Author: Arthur Erdélyi
Publisher: American Mathematical Soc.
Published: 1957
Total Pages: 60
ISBN-13: 0821812254
DOWNLOAD EBOOKAsymptotics and Special Functions
Author: F. W. J. Olver
Publisher: Academic Press
Published: 2014-05-10
Total Pages: 589
ISBN-13: 148326744X
DOWNLOAD EBOOKAsymptotics 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.
Asymptotics and Special Functions
Author: Frank Olver
Publisher: CRC Press
Published: 1997-01-24
Total Pages: 591
ISBN-13: 1439864543
DOWNLOAD EBOOKA 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.
Selected Papers of F.W.J. Olver
Author: Frank W. J. Olver
Publisher: World Scientific
Published: 2000
Total Pages: 548
ISBN-13: 9789810249946
DOWNLOAD EBOOKAsymptotic Approximations of Integrals
Author: R. Wong
Publisher: SIAM
Published: 2001-01-01
Total Pages: 560
ISBN-13: 9780898719260
DOWNLOAD EBOOKAsymptotic methods are frequently used in many branches of both pure and applied mathematics, and this classic text remains the most up-to-date book dealing with one important aspect of this area, namely, asymptotic approximations of integrals. In Asymptotic Approximations of Integrals, all results are proved rigorously, and many of the approximation formulas are accompanied by error bounds. A thorough discussion on multidimensional integrals is given, and references are provided. The book contains the "distributional method," which is not available elsewhere. Most of the examples in this text come from concrete applications. Since its publication twelve years ago, significant developments have occurred in the general theory of asymptotic expansions, including smoothing of the Stokes phenomenon, uniform exponentially improved asymptotic expansions, and hyperasymptotics. These new concepts belong to the area now known as "exponential asymptotics." Expositions of these new theories are available in papers published in various journals, but not yet in book form. Audience: this book can be used either as a text for graduate students in mathematics, physics, and engineering or as a reference for research workers in these fields.
Asymptotic Methods For Integrals
Author: Nico M Temme
Publisher: World Scientific
Published: 2014-10-31
Total Pages: 628
ISBN-13: 9814612170
DOWNLOAD EBOOKThis book gives introductory chapters on the classical basic and standard methods for asymptotic analysis, such as Watson's lemma, Laplace's method, the saddle point and steepest descent methods, stationary phase and Darboux's method. The methods, explained in great detail, will obtain asymptotic approximations of the well-known special functions of mathematical physics and probability theory. After these introductory chapters, the methods of uniform asymptotic analysis are described in which several parameters have influence on typical phenomena: turning points and transition points, coinciding saddle and singularities. In all these examples, the special functions are indicated that describe the peculiar behavior of the integrals.The text extensively covers the classical methods with an emphasis on how to obtain expansions, and how to use the results for numerical methods, in particular for approximating special functions. In this way, we work with a computational mind: how can we use certain expansions in numerical analysis and in computer programs, how can we compute coefficients, and so on.
Theory and Application of Special Functions
Author: Richard Askey
Publisher: Academic Press
Published: 2014-05-10
Total Pages: 573
ISBN-13: 1483216160
DOWNLOAD EBOOKTheory and Application of Special Functions contains the proceedings of the Advanced Seminar on Special Functions sponsored by the Mathematics Research Center of the University of Wisconsin-Madison and held from March 31 to April 2, 1975. The seminar tackled the theory and application of special functions and covered topics ranging from the asymptotic estimation of special functions to association schemes and coding theory. Some interesting results, conjectures, and problems are given. Comprised of 13 chapters, this book begins with a survey of computational methods in special functions, followed by a discussion on unsolved problems in the asymptotic estimation of special functions. The reader is then introduced to periodic Bernoulli numbers, summation formulas, and applications; problems and prospects for basic hypergeometric functions; and linear growth models with many types and multidimensional Hahn polynomials. Subsequent chapters explore two-variable analogues of the classical orthogonal polynomials; special functions of matrix and single argument in statistics; and some properties of the determinants of orthogonal polynomials. This monograph is intended primarily for students and practitioners of mathematics.
Special Functions
Author: Nico M. Temme
Publisher: John Wiley & Sons
Published: 2011-03-01
Total Pages: 392
ISBN-13: 1118030818
DOWNLOAD EBOOKThis 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.
Asymptotic and Computational Analysis
Author: R. Wong
Publisher: CRC Press
Published: 2020-12-17
Total Pages: 782
ISBN-13: 1000154130
DOWNLOAD EBOOKPapers presented at the International Symposium on Asymptotic and Computational Analysis, held June 1989, Winnipeg, Man., sponsored by the Dept. of Applied Mathematics, University of Manitoba and the Canadian Applied Mathematics Society.
