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.

• 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

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.

• 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

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.

• 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