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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
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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

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