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Author: Gertrude Blanch
Publisher:
ISBN:
Category : Functions
Languages : en
Pages : 28
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Book Description
Author: Gertrude Blanch
Publisher:
ISBN:
Category : Functions
Languages : en
Pages : 28
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Book Description
Author: Andrew Peterson
Publisher: Springer Nature
ISBN: 303101717X
Category : Technology & Engineering
Languages : en
Pages : 123
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Book Description
This lecture presents a modern approach for the computation of Mathieu functions. These functions find application in boundary value analysis such as electromagnetic scattering from elliptic cylinders and flat strips, as well as the analogous acoustic and optical problems, and many other applications in science and engineering. The authors review the traditional approach used for these functions, show its limitations, and provide an alternative "tuned" approach enabling improved accuracy and convergence. The performance of this approach is investigated for a wide range of parameters and machine precision. Examples from electromagnetic scattering are provided for illustration and to show the convergence of the typical series that employ Mathieu functions for boundary value analysis.
Author: Shanjie Zhang
Publisher: Wiley-Interscience
ISBN:
Category : Computers
Languages : en
Pages : 752
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Book Description
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.
Author: Wolfgang Schweizer
Publisher: Springer Nature
ISBN: 3030642321
Category : Science
Languages : en
Pages : 282
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Book Description
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.
Author: Milton Abramowitz
Publisher: Courier Corporation
ISBN: 9780486612720
Category : Mathematics
Languages : en
Pages : 1068
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Book Description
An extensive summary of mathematical functions that occur in physical and engineering problems
Author: Wilhelm Magnus
Publisher: Courier Corporation
ISBN: 0486150291
Category : Mathematics
Languages : en
Pages : 148
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Book Description
This two-part treatment explains basic theory and details, including oscillatory solutions, intervals of stability and instability, discriminants, and coexistence. Particular attention to stability problems and coexistence of periodic solutions. 1966 edition.
Author: Gertrude Blanch
Publisher:
ISBN:
Category : Eigenvalues
Languages : en
Pages : 304
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Book Description
Author: F. M. Arscott
Publisher: Elsevier
ISBN: 1483164888
Category : Mathematics
Languages : en
Pages : 295
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Book Description
Periodic Differential Equations: An Introduction to Mathieu, Lamé, and Allied Functions covers the fundamental problems and techniques of solution of periodic differential equations. This book is composed of 10 chapters that present important equations and the special functions they generate, ranging from Mathieu's equation to the intractable ellipsoidal wave equation. This book starts with a survey of the main problems related to the formation of periodic differential equations. The subsequent chapters deal with the general theory of Mathieu's equation, Mathieu functions of integral order, and the principles of asymptotic expansions. These topics are followed by discussions of the stable and unstable solutions of Mathieu's general equation; general properties and characteristic exponent of Hill's equation; and the general nature and solutions of the spheroidal wave equation. The concluding chapters explore the polynomials, orthogonality properties, and integral relations of Lamé's equation. These chapters also describe the wave functions and solutions of the ellipsoidal wave equation. This book will prove useful to pure and applied mathematicians and functional analysis.
Author: John P. Boyd
Publisher: Courier Corporation
ISBN: 0486411834
Category : Mathematics
Languages : en
Pages : 690
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Book Description
Completely revised text focuses on use of spectral methods to solve boundary value, eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions, as well as cardinal functions, linear eigenvalue problems, matrix-solving methods, coordinate transformations, methods for unbounded intervals, spherical and cylindrical geometry, and much more. 7 Appendices. Glossary. Bibliography. Index. Over 160 text figures.
Author: Aerospace Research Laboratories (U.S.)
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages :
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Book Description
