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!

Homework Help: Gamma function induction

  1. Nov 30, 2011 #1
    1. The problem statement, all variables and given/known data

    Prove by induction that gamma(v+1)(v+1)(v+2)...(v+k)=gamma(v+k+1) for k=1,2,3...

    2. Relevant equations

    Really just using the relation x*gamma(x)=gamma(x+1)

    3. The attempt at a solution

    for a basis gamma(v+1)(v+1)=gamma(v+1+1)
    so holds for k = 1

    inductive hypothesis

    now for k = n+1 i get

    but what confuses me is if i use the above relationship, then gamma(v+n+2) should equal (v+n+1)*gamma(v+n+1), unfortunately my proof claims it's equal to gamma(v+1)(v+n+1). I'm lost at this step
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Nov 30, 2011 #2
    Your inductive hypothesis is wrong.

    It should be gamma(v+1)(v+1)(v+2)...(v+k)=gamma(v+k+1) for some k.
    Your inductive step then is gamma(v+1)(v+1)(v+2)...(v+k)(v+k+1)=gamma(v+k+2).
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook