1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Any help understanding this Lemma is Appreciated!

  1. Mar 12, 2012 #1
    The lemma and proof are attached, how does the hypothesis imply that ∫h(u)*p(u)du = 0. This is where I am hung up. I don't see how the hypothesis implies this, please help!

    Thanks in advance,

    Mining_Engr
     

    Attached Files:

  2. jcsd
  3. Mar 12, 2012 #2

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    p(u) is a polynomial, say
    [tex] p(u) = \sum_{i=0}^n \alpha_i u^i[/tex]

    then
    [tex] \int h(u) p(u) du = \int h(u) \sum_{i=0}^n \alpha_i u^i du = \sum_{i=0}^n \alpha_i \int h(u) u^i du [/tex]
    and all those integrals at the end are zero so the whole sum is zero
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook