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Contains papers presented at the International Symposium on Asymptotic and Computational Analysis, held in June 1989 in Winnipeg, Manitoba, sponsored by the Department of Applied Mathematics, University of Manitoba and the Canadian Applied Mathematics Society.
Contains papers presented at the International Symposium on Asymptotic and Computational Analysis, held in June 1989 in Winnipeg, Manitoba, sponsored by the Department of Applied Mathematics, University of Manitoba and the Canadian Applied Mathematics Society.
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R. WONG is Professor and Head of the Department of Applied Mathematics, University of Manitoba, Winnipeg, Canada. The author of Asymptotic Approximations of Integrals, and the author or coauthor of over 50 mathematical journal articles, Dr. Wong is President of the Canadian Applied Mathematics Society and a member of the Society for Industrial and Applied Mathematics. He received the B.A. degree (1965) in mathematics from San Diego State College, San Diego, California, and Ph.D. degree (1969) in mathematics from the University of Alberta, Edmonton, Canada.
Inhaltsangabe
Preface Contributors INVITED PAPERS Graphs as an Aid to Understanding Special Functions /by R. A. Askey Asymptotics of Integals, Series, and Operators /by L. Berg Asymptotic Expansions for the Coefficient Functions Associated with Linear Second Order Differential Equations: The Simple Pole Case /by W. G. C. Boyd Landen Transformations of Integrals /by B. C. Carlson Accelerating the Convergence of Chebyshev Series /by L. M. Ciasullo and J, A. Cochran Practical Methods for the Uniform Asymptotic Evaluation of Oscillating Integrals with Several Coalescing Saddle Points /by J. N. L. Connor New Inequalities for the Zeros of Confluent Hypergeometric Functions /by Luigi Gatteschi How (Un)stable Are Vandermonde Systems? /by Walter Gautschi Singular Point and Exponential Asymptotics /by Floyd B. Hanson Uniform Asymptotic Remainders /by D. S. Jones Period Tripling and Subharmonic Oscillations in Marangoni Flows in a Cylindrical Liquid Bridge /by Nicholas D. Kazarinoff and Joseph S. Wilkowski Positive Solutions for Degenerate and Nondegenerate Elliptic Systems: Existence and Numerical Approximations /by Anthony W. Leung and Guangwei Fan Observable Tunneling in Several Dimensions /by R. E. Meyer On Stokes' Phenomenon and Converging Factors /by Frank W. J. Olver Singularly Perturbed Boundary Value Problems Viewed in the Lienard Plane /by J. D. Allen and R. E. O'Malley, Jr. On the Asymptotic Theory of the Orr Sommerfeld Problem /by W. H. Reid Gevrey Property of Formal Solutions in a Parameter /by Yasutaka Sibuya A Riccati Approach to the Airy Equation /by Donald R. Smith A System of Polynomials Associated with the Chester, Friedman, and Ursell Technique /by K. Soni and R. P. Soni Rational Approximation of the Step, Filter, and Impulse Functions /by Yasuhiko Ikebe, Marek Kowalski, and Frank Stenger Polynomial Asymptotic Estimates of Gegenbauer, Laguerre, and Jacobi Polynomials /by Nico M. Temme Integrals with a Large Parameter and the Maximum Modulus Principle /by F. Ursell Finite Axial Extension and Torsion of Elasti~ Helicoidal Shells /by Frederic Y. M. Wan Some Properties of Convolution Sequences and Asymptotics for the Taylor Coefficients for Products of Bessel Functions /by Jet Wimp A Generalization of Olver's Algorithm for Linear Difference Systems /by R. V. M. Zahar CONTRIBUTED PAPERS Continental Shelf Wave Scattering: Partial Removal of the Rigid Lid /by Anthony M. J. Davis Some Aspects of Invariant Subspaces Computation /by Luca Dieci and Robert D. Russell Error Bounds via Complete Monotonicity for a Uniform Asymptotic Expansion of the Legendre Function p~m(cosh z) /by C. L. Frenzen Computational Asymptotics of Fourth Order Operators /by P. A. Carinhas and S. A. Fulling Universal Asymptotic Distribution Functions mod 1 /by William M. Y. Goh and Eric Schmutz On the n Variable Saddle Point and Steepest Descent Methods /by D. Kaminski Applications of the Method of Steepest Descents in WavePropagation Problems /by Francesco Mainardi and Giuliano Vitali The Asymptotics of Pearcey's Integral for Complex Variables /by R. B. Paris Asymptotic Methods in Magnetoconvection /by N. Rudraiah, O. P. Chandna ,and R. M. Barron The Interior Layer Structure for a Linear Parabolic Problem with Discontinuous Data /by Shagi Di Shih Asymptotic Expansions of Solutions to ~u u = f at Infinity /by D. Siegel Approximating Zeros of Solutions of Second Order Linear ODEs by "Phase Function" Methods /by R. Spigler and M. Vianello Asymptotic Expansions of Integrals of Two Bessel Functions /by B. J. Stoyanov, R. A. Farrell, and J. F. Bird On Eigenvalues with Exponentially Small Imaginary Part /by A. D. Wood and R. B. Paris Index
Preface Contributors INVITED PAPERS Graphs as an Aid to Understanding Special Functions /by R. A. Askey Asymptotics of Integals, Series, and Operators /by L. Berg Asymptotic Expansions for the Coefficient Functions Associated with Linear Second Order Differential Equations: The Simple Pole Case /by W. G. C. Boyd Landen Transformations of Integrals /by B. C. Carlson Accelerating the Convergence of Chebyshev Series /by L. M. Ciasullo and J, A. Cochran Practical Methods for the Uniform Asymptotic Evaluation of Oscillating Integrals with Several Coalescing Saddle Points /by J. N. L. Connor New Inequalities for the Zeros of Confluent Hypergeometric Functions /by Luigi Gatteschi How (Un)stable Are Vandermonde Systems? /by Walter Gautschi Singular Point and Exponential Asymptotics /by Floyd B. Hanson Uniform Asymptotic Remainders /by D. S. Jones Period Tripling and Subharmonic Oscillations in Marangoni Flows in a Cylindrical Liquid Bridge /by Nicholas D. Kazarinoff and Joseph S. Wilkowski Positive Solutions for Degenerate and Nondegenerate Elliptic Systems: Existence and Numerical Approximations /by Anthony W. Leung and Guangwei Fan Observable Tunneling in Several Dimensions /by R. E. Meyer On Stokes' Phenomenon and Converging Factors /by Frank W. J. Olver Singularly Perturbed Boundary Value Problems Viewed in the Lienard Plane /by J. D. Allen and R. E. O'Malley, Jr. On the Asymptotic Theory of the Orr Sommerfeld Problem /by W. H. Reid Gevrey Property of Formal Solutions in a Parameter /by Yasutaka Sibuya A Riccati Approach to the Airy Equation /by Donald R. Smith A System of Polynomials Associated with the Chester, Friedman, and Ursell Technique /by K. Soni and R. P. Soni Rational Approximation of the Step, Filter, and Impulse Functions /by Yasuhiko Ikebe, Marek Kowalski, and Frank Stenger Polynomial Asymptotic Estimates of Gegenbauer, Laguerre, and Jacobi Polynomials /by Nico M. Temme Integrals with a Large Parameter and the Maximum Modulus Principle /by F. Ursell Finite Axial Extension and Torsion of Elasti~ Helicoidal Shells /by Frederic Y. M. Wan Some Properties of Convolution Sequences and Asymptotics for the Taylor Coefficients for Products of Bessel Functions /by Jet Wimp A Generalization of Olver's Algorithm for Linear Difference Systems /by R. V. M. Zahar CONTRIBUTED PAPERS Continental Shelf Wave Scattering: Partial Removal of the Rigid Lid /by Anthony M. J. Davis Some Aspects of Invariant Subspaces Computation /by Luca Dieci and Robert D. Russell Error Bounds via Complete Monotonicity for a Uniform Asymptotic Expansion of the Legendre Function p~m(cosh z) /by C. L. Frenzen Computational Asymptotics of Fourth Order Operators /by P. A. Carinhas and S. A. Fulling Universal Asymptotic Distribution Functions mod 1 /by William M. Y. Goh and Eric Schmutz On the n Variable Saddle Point and Steepest Descent Methods /by D. Kaminski Applications of the Method of Steepest Descents in WavePropagation Problems /by Francesco Mainardi and Giuliano Vitali The Asymptotics of Pearcey's Integral for Complex Variables /by R. B. Paris Asymptotic Methods in Magnetoconvection /by N. Rudraiah, O. P. Chandna ,and R. M. Barron The Interior Layer Structure for a Linear Parabolic Problem with Discontinuous Data /by Shagi Di Shih Asymptotic Expansions of Solutions to ~u u = f at Infinity /by D. Siegel Approximating Zeros of Solutions of Second Order Linear ODEs by "Phase Function" Methods /by R. Spigler and M. Vianello Asymptotic Expansions of Integrals of Two Bessel Functions /by B. J. Stoyanov, R. A. Farrell, and J. F. Bird On Eigenvalues with Exponentially Small Imaginary Part /by A. D. Wood and R. B. Paris Index
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