(adsbygoogle = window.adsbygoogle || []).push({}); Beyond "Saddle point" method

Let's suppose we have an integral:

[tex] \int_{-\infty}^{\infty}dXe^{-sF(X)}=g(s) [/tex]

where [tex] X=(x_1,x_2,x_3,....,x_n) [/tex]

Then for big s we could use "Saddle point method " and all that stuff well, we still have the problem in finding a "meaning" for g(s) for every positive s, the idea i had (of course i know it has ben named before ) is appart from making the expansion near the "stationary points" so [tex] dF(X)=0 [/tex] is to evaluate in some "wise" points satisfying some other constraint, i.e [tex] dF(X)+F(x)=0 [/tex] or something similar, the idea came to me when examining "Gaussian Cuadrature" where you evalute your function plus a weight function at certain points that are the roots of Laguerre/Hermite?¿ (i can't remember ) my idea is if something similar can be made to give meaning to the inegral g(s) for s>0 BUT not big (let's say s=1) or for example imposing an extra "multiplier" so the integral becomes:

[tex] \int_{-\infty}^{\infty}dXe^{-sF(X)-s\lambda g(X)}=g(s) [/tex]

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Beyond Saddle point method

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**