Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-23T07:42:23.738Z Has data issue: false hasContentIssue false
  • English
  • Français

A recursion formula for the coefficients in an asymptotic expansion

Published online by Cambridge University Press:  18 May 2009

E. M. Wright
E. M. Wright
Affiliation:
The University Aberdeen
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Many authors have proved results deducing an asymptotic expansion of

for large from the behaviour of f(t), when f(t) is regular in an appropriate part of the complex t-plane. For example, if, for some k > 0 and some Am, αm

for all large such that R(t) > C, then, as ⃗ ∞ in a suitable sector in the z-plane, we have

where Z is an appropriate value of z1/z.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 4 , Issue 1 , December 1958 , pp. 38 - 41
Copyright
Copyright © Glasgow Mathematical Journal Trust 1958

References

1.Ford, W. B., The asymptotic developments of functions defined by Maclaurin series (Ann Arbor, 1936).CrossRefGoogle Scholar
2.Hughes, H. K., Bull. American Math. Soc., 50 (1944), 425–430.CrossRefGoogle Scholar
3.Jordan, C., Calculus of finite differences (2nd edn., New York, 1947), 168–179.Google Scholar
4.Riney, T. D., Proc. Amer. Math. Soc., 7 (1956), 245–9.CrossRefGoogle Scholar
5.Riney, T. D., Trans. American Math. Soc., 88 (1958), 214–226.CrossRefGoogle Scholar
6.Wright, E. M., J. London Math. Soc., 10 (1935), 287–293; see also correction, Trans. American Math. Soc. 27 (1952), 256.Google Scholar
7.Wright, E. M., Phil. Trans. Roy. Soc., A238 (1940), 423–451 and A239 (1941), 217–232.Google Scholar
8.Wright, E. M., Trans. American Math. Soc., 64 (1948), 409–438.CrossRefGoogle Scholar