What is "Watson's Lemma on Laplace Transforms"?

Answer 1

Watsons Lemma has to do with the relationship between the behavior of a function in the neighborhood of the origin and the behavior of its Laplace transform

If

f(t) < Me^(at)

and if, in some neighborhood of t=0 the function f(t) has a Maclaurin polynomial expansion given as

sum (cr*t^r)/(r!)

where r runs from 0 to ∞ (and the cr are the Maclaurin coefficients of the polynomial expansion) then the LaPlace transform of f(t) has an asymptotic expansion of the form

F(z) ≈ sum cr*z^(-r-1)

as r runs from 0 to ∞

It's really just a generalization of the Tauberian theorems.


Doug

Answer 2

Here is your answer to what...

Coherent, systematic coverage of standard methods: integration by parts, Watson s lemma, LaPlace s method, stationary phase and steepest descents. Also treated are the Mellin transform method and less elementary aspects of the method of steepest descents.

Answer 3

http://math.arizona.edu/~lega/583/Spring99/lectnotes/AE2.html