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

Is there a proof for this?

  1. Mar 25, 2009 #1

    let's say we have two functions of two variables: f(x,y) and g(x,y). Say we know that the sum / integral over all y's of f^n * g does not depend on x for every natural number n (and zero). Does that mean that f and g both don't depend on x?

  2. jcsd
  3. Mar 25, 2009 #2


    User Avatar
    Science Advisor

    Not necessarily. Let g(x,y)= 0 for all x and y. Then f^n*g (I assume you mean composition) is f^n(0) for all x and y so the sum/integral is a constant no matter what f is. If f^n*g is ordinary multiplication of functions, then f^n*g= 0 for all x and y and again, the integral is a constant no matter what f is.
  4. Mar 25, 2009 #3


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    If it's composition, then g better be a vector
  5. Mar 25, 2009 #4
    Sorry for not being clear - f(x,y) and g(x,y) are scalar functions and * is ordinary multiplication. f^n is then f multiplied n times by itself. Now, if we don't assume the trivial null solution, f(x,y)=0 or g(x,y)=0, does my statement hold?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook