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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
    gamma(v+1)(v+n)=gamma(v+n+1)

    now for k = n+1 i get
    gamma(v+1)(v+n+1)=gamma(v+n+2)

    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).
    Alright?
     
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