Special Issue: Dedicated to the Memory of Frank Olver (Part I)No Access

Mathematics that has intrigued me

F. W. J. Olver

https://doi.org/10.1142/S0219530514500262Cited by:0 (Source: Crossref)

Abstract

I trace the main steps of the first fifty-five years of my career as an applied mathematician, pausing from time to time to describe problems that arose in asymptotics and numerical analysis and had far-reaching effects on this career.

Lecture delivered at Asymptotics and Applied Analysis, Conference in Honor of Frank W. J. Olver's 75th Birthday, January 10–14, 2000, San Diego State University, San Diego, California.

Editors' Note: Frank W. J. Olver died on April 23, 2013. The following text was typed by his son, Peter J. Olver, from handwritten notes found among his papers. At times the writing is unpolished, including incomplete sentences, but the editors have decided to leave it essentially the way it was written. However, for clarity, some abbreviations have been written out in full. A couple of handwritten words could not be deciphered, and a guess for what was intended is enclosed in brackets: […]. Endnotes have been made into footnotes within the body of the article. References were mostly not included in the handwritten text, but rather listed in order at the end. Citations to references have been included at the appropriate point in the text.

Keywords:

AMSC: 33-00, 33F05, 34M30, 34M40, 39A06, 65D20, 65G05

References

J. R. Airey, The "converging factor" in asymptotic series and the calculation of Bessel, Laguerre and other functions, Phil. Mag. (7) 24 (1937) 521–552 . Google Scholar
F. Benford , Proc. Amer. Philos. Soc. 78 , 551 ( 1938 ) . Google Scholar
M. V. Berry , Proc. R. Soc. Lond. A 422 , 7 ( 1989 ) . Crossref, Web of Science, Google Scholar
G. D. Birkhoff , Trans. Amer. Math. Soc. 12 , 243 ( 1911 ) . Crossref, Google Scholar
G. D. Birkhoff , Acta Math. 54 , 205 ( 1930 ) . Crossref, Google Scholar
G. D. Birkhoff and W. J. Trjitzinsky , Acta Math. 60 , 1 ( 1932 ) . Crossref, Google Scholar
British Association for the Advancement of Science, Bessel Functions — Part II, Mathematical Tables, Vol. 10 (Cambridge University Press, Cambridge, 1952) . Google Scholar
S. J. Chapman et al. , SIAM Rev. 41 , 417 ( 1999 ) . Crossref, Web of Science, Google Scholar
C. W. Clenshaw and F. W. J. Olver , J. Assoc. Comput. Mach. 31 , 319 ( 1984 ) . Crossref, Web of Science, Google Scholar
E. T. Copson , Theory of Functions of a Complex Variable ( Oxford University Press , London , 1935 ) . Google Scholar
E. T. Copson, The asymptotic expansion of a function defined by a definite integral or a contour integral, S.R.E./ACS Report No. 106, Department of Scientific Research and Experiment, London (1946) . Google Scholar
N. G. De Bruijn , Asymptotic Methods in Analysis , 2nd edn. ( North-Holland , Amsterdam , 1961 ) . Google Scholar
R. B. Dingle , Asymptotics Expansions: Their Derivation and Interpretation ( Academic Press , London , 1973 ) . Google Scholar
A. Erdélyi , Asymptotics Expansions ( Dover , New York , 1956 ) . Google Scholar
A. Erdélyi and M. Wyman , Arch. Ration. Mech. Anal. 14 , 217 ( 1963 ) . Crossref, Web of Science, Google Scholar
H. M. Nautical Almanac Office, Interpolation and Allied Tables (H.M. Stationery Office, London, 1956) . Google Scholar
D. W. Lozier, Numerical solution of second-order linear difference equations, Report No. NBSIR 80-1976, National Bureau of Standards, US Department of Commerce, Washington, D.C. (1980) . Google Scholar
D. W. Lozier and F. W. J. Olver , SIAM J. Numer. Anal. 27 , 1295 ( 1990 ) . Crossref, Web of Science, Google Scholar
W. E. Milne , Numerical Solution of Differential Equations ( Wiley , New York , 1953 ) . Google Scholar
J. C. P. Miller , Math. Proc. Cambridge Philos. Soc. 48 , 243 ( 1952 ) . Crossref, Web of Science, Google Scholar
L. M. Milne-Thompson , The Calculus of Finite Differences ( Macmillan , London , 1933 ) . Google Scholar
M. Abramowitz and I. A. Stegun (eds.) , Handbook of Mathematical Functions , Applied Mathematics Series ( US Government Printing Office , Washington, D.C. , 1964 ) . Google Scholar
A. B. Olde Daalhuis , Proc. R. Soc. Lond. A 454 , 1 ( 1998 ) . Crossref, Web of Science, Google Scholar
F. W. J. Olver , J. Res. Natl. Bur. Stand. B, Math. Math. Phys. 71 , 111 ( 1967 ) . Crossref, Google Scholar
F. W. J. Olver, Asymptotics and Special Functions (Academic Press, New York, 1974); Reprinted in 1997 by AK Peters, Wellesley, MA . Google Scholar
F. W. J. Olver , SIAM Rev. 22 , 188 ( 1980 ) . Crossref, Web of Science, Google Scholar
F. W. J. Olver, Wave Asymptotics, eds. P. A. Martin and G. R. Wickham (Cambridge University Press, Cambridge, 1991) pp. 54–68. Google Scholar
F. W. J. Olver, Resurgence in difference equations, with an application to Legendre functions, Proc. Int. Workshop on Special Functions (City University of Hong Kong, Hong Kong, 1999) pp. 221–235. Google Scholar
F. W. J. Olver et al. (eds.) , NIST Handbook of Mathematical Functions ( Cambridge University Press , Cambridge , 2010 ) . Google Scholar
E. Ja. Riekstiņš , Latvian Math. Yearbook 5 ( 1966 ) . Google Scholar
T. J. Stieltjes , Ann. Sci. École Norm. Sup. (3) 3 , 201 ( 1886 ) . Crossref, Google Scholar
G. G. Stokes , Trans. Cambridge Philos. Soc. 10 , 105 ( 1857 ) . Google Scholar
P. R. Turner , IMA J. Numer. Anal. 2 , 407 ( 1982 ) . Crossref, Web of Science, Google Scholar
P. R. Turner , IMA J. Numer. Anal. 4 , 225 ( 1984 ) . Crossref, Web of Science, Google Scholar
G. N. Watson , Phil. Trans. R. Soc. Lond. A 211 , 279 ( 1911 ) . Crossref, Google Scholar
G. N. Watson , A Treatise on the Theory of Bessel Functions , 2nd edn. ( Cambridge University Press , Cambridge , 1944 ) . Google Scholar
E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, 4th edn. (Cambridge University Press, Cambridge, 1927). Google Scholar
R. Wong and H. Li , J. Comput. Appl. Math. 41 , 65 ( 1992 ) . Crossref, Web of Science, Google Scholar
R. Wong and H. Li , Studies Appl. Math. 87 , 289 ( 1992 ) . Crossref, Web of Science, Google Scholar
M. Wyman , Canad. J. Math. 15 , 332 ( 1963 ) . Crossref, Web of Science, Google Scholar