Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Circle method for Laplace transform.

  1. Apr 2, 2007 #1


    User Avatar

    If we have the Laplace transform:

    [tex] \int_{0}^{\infty}dtf(t)exp(-st) = \sum_{n=0}^{\infty}(f(n)-f(n-1))\frac{exp(-sn)}{s}=g(s) [/tex]

    (We have used Abel sum formula on the right hand)

    then making Z=exp(s) we find the Z-transform:

    [tex] \sum_{n=0}^{\infty}(f(n)-f(n-1))Z^{-n} [/tex]

    which can be inverted to get:

    [tex] 2\pi i (f(n)-f(n-1))=\oint g(lnZ) (lnZ)Z^{n-1} [/tex]

    my quetion is if using 'Circle method' you can get an asymptotic expansion for: [tex] f(n)-f(n-1) [/tex] n big, also another question if we have that:

    [tex] f(n)-f(n-1) \sim h(n) [/tex] then ??? [tex] f(n) \sim \int h(n)dn [/tex]
    Last edited: Apr 2, 2007
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted

Similar Threads for Circle method Laplace
I Econometrics regression method