# Asymptotic homework help

1. May 14, 2007

### tpm

For x-->oo (big) is there a relationship between

A) $$\oint_{C}ds F(s) exp(sx)$$

and

B) $$\oint_{C}ds exp(as^{2}) exp(sx)$$

Where the exponential of $$s^{2}$$ is the result of expanding the function

$$e^{logF(s)}$$ near its maximum/minimum.

'C' is the contour defined by (c-ioo , c+ioo) for a real c so all the singularities lie on the left of Re(s)=c

I believe (but can't proof) that for big x the quotient A/B tends to 1 but not pretty sure, or if i must introduce any change, any help would be appreciated

Last edited: May 14, 2007