Proving the Inductive Relationship for the Gamma Function

[medeski]

Homework Statement

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

Homework Equations

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

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

 

[susskind_leon]

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?