Asymptotics For Solutions Of Linear Differential Equations Having Turning Points With Applications
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Asymptotics For Solutions Of Linear Differential Equations Having Turning Points With Applications
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Author : Shlomo Strelitz
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Asymptotics For Solutions Of Linear Differential Equations Having Turning Points With Applications written by Shlomo Strelitz and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
Asymptotics are built for the solutions $y_j(x, \lambda)$, $y_j DEGREES{(k)}(0, \lambda)=\delta_{j\, n-k}$, $0\le j, k+1\le n$ of the equation $L(y)=\lambda p(x)y, \quad x\in [0,1], $ where $L(y)$ is a linear differential operator of whatever order $n\ge 2$ and $p(x)$ is assumed to possess a finite number of turning points. The established asymptotics are afterwards applied to the study of: 1) the existence of infinite eigenvalue sequences for various multipoint boundary problems posed on $L(y)=\lambda p(x)y, \quad x\in [0,1], $, especially as $n=2$ and $n=3$ (let us be aware that the same method can be successfully applied on many occasions in case $n>3$ too) and 2) asymptotical distribution of the corresponding eigenvalue sequences on the
Asymptotics For Solutions Of Linear Differential Equations Having Turning Points With Applications
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Author : Shlomo Strelitz
language : en
Publisher: American Mathematical Society(RI)
Release Date : 2014-09-11
Asymptotics For Solutions Of Linear Differential Equations Having Turning Points With Applications written by Shlomo Strelitz and has been published by American Mathematical Society(RI) this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-11 with Differential equations, Linear categories.
Asymptotics are built for the solutions $y_j(x, \lambda)$, $y_j DEGREES{(k)}(0, \lambda)=\delta_{j\, n-k}$, $0\le j, k+1\le n$ of the equation $L(y)=\lambda p(x)y, \quad x\in [0,1], $ where $L(y)$ is a linear differential operator of whatever order $n\ge 2$ and $p(x)$ is assumed to possess a finite number of turning points. The established asymptotics are afterwards applied to the study of: 1) the existence of infinite eigenvalue sequences for various multipoint boundary problems posed on $L(y)=\lambda p(x)y, \quad x\in [0,1], $, especially as $n=2$ and $n=3$ (let us be aware that the same method can be successfully applied on many occasions in case $n>3$ too) and 2) asymptotical distribution of the corresponding eigenvalue sequences on the
Asymptotics And Special Functions
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Author : Frank Olver
language : en
Publisher: CRC Press
Release Date : 1997-01-24
Asymptotics And Special Functions written by Frank Olver and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-24 with Mathematics categories.
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.
Asymptotics And Special Functions
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Author : F. W. J. Olver
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Asymptotics And Special Functions written by F. W. J. Olver and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
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.
Asymptotic Expansions For Ordinary Differential Equations
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Author : Wolfgang Wasow
language : en
Publisher: Courier Dover Publications
Release Date : 2018-03-21
Asymptotic Expansions For Ordinary Differential Equations written by Wolfgang Wasow and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-21 with Mathematics categories.
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.
Asymptotic Solutions Of Differential Equations And Their Applications
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Author : Calvin Hayden Wilcox
language : en
Publisher:
Release Date : 1964
Asymptotic Solutions Of Differential Equations And Their Applications written by Calvin Hayden Wilcox and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with Mathematics categories.
Journal Of Research Of The National Bureau Of Standards
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Author :
language : en
Publisher:
Release Date : 1965
Journal Of Research Of The National Bureau Of Standards written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Engineering categories.
Nist Handbook Of Mathematical Functions Hardback And Cd Rom
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Author : Frank W. J. Olver
language : en
Publisher: Cambridge University Press
Release Date : 2010-05-17
Nist Handbook Of Mathematical Functions Hardback And Cd Rom written by Frank W. J. Olver and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-17 with Mathematics categories.
The new standard reference on mathematical functions, replacing the classic but outdated handbook from Abramowitz and Stegun. Includes PDF version.
Introduction To Asymptotics And Special Functions
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Author : F. W. J. Olver
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Introduction To Asymptotics And Special Functions written by F. W. J. Olver and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
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.
Walter Gautschi Volume 1
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Author : Claude Brezinski
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-22
Walter Gautschi Volume 1 written by Claude Brezinski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-22 with Mathematics categories.
Walter Gautschi has written extensively on topics ranging from special functions, quadrature and orthogonal polynomials to difference and differential equations, software implementations, and the history of mathematics. He is world renowned for his pioneering work in numerical analysis and constructive orthogonal polynomials, including a definitive textbook in the former, and a monograph in the latter area. This three-volume set, Walter Gautschi: Selected Works with Commentaries, is a compilation of Gautschi’s most influential papers and includes commentaries by leading experts. The work begins with a detailed biographical section and ends with a section commemorating Walter’s prematurely deceased twin brother. This title will appeal to graduate students and researchers in numerical analysis, as well as to historians of science. Selected Works with Commentaries, Vol. 1 Numerical Conditioning Special Functions Interpolation and Approximation Selected Works with Commentaries, Vol. 2 Orthogonal Polynomials on the Real Line Orthogonal Polynomials on the Semicircle Chebyshev Quadrature Kronrod and Other Quadratures Gauss-type Quadrature Selected Works with Commentaries, Vol. 3 Linear Difference Equations Ordinary Differential Equations Software History and Biography Miscellanea Works of Werner Gautschi