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

Iterative integration in several variables

  1. Jul 1, 2011 #1
    as a physicist , there are some integrals in several variables that are DIVERGENT

    in order to regularize them i argue that for any integral in several variables

    [tex] \int_{V} f(x,y,z)dV [/tex]

    you can always perform an interative integration (you integrate in variable 'x' for example keeping the others variables as constant and then you regularize the result in each variable by using the Hadamard's finite part integral definition)

    but is this valid ?? .. even for a divergent integral (let us suppose we introduce a cut-off so the integral is rendered finite and then we take the cut-off limit --> oo ) is this valid we can perform an integral in several variables by doing an interation of one dimensional integrals ??

    let us suppose i introduce the regulators [tex] ((x+a)((y+b)(z+c))^{-s} [/tex]

    for a big 's' so the integral is convergent and then i take the limit (by analytic continuation ) to s -->0
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?