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Question Number 2340 by Yozzi last updated on 18/Nov/15
Prove that, ∀m∈Z^+ , Π_(r=1) ^m Γ(x+((r−1)/m))=m^((1/2)−mx) (2π)^((m−1)/2) Γ(mx). {Γ(x)=∫_0 ^∞ t^(x−1) e^(−t) dt, x>0}
Provethat,∀m∈Z+,∏mr=1Γ(x+r−1m)=m12−mx(2π)m−12Γ(mx).{Γ(x)=∫0∞tx−1e−tdt,x>0}
Commented by prakash jain last updated on 18/Nov/15
Π_(r=1) ^m Γ((r/(m+1)))=(√(((2π)^m )/(m+1))) can be used to prove.
∏mr=1Γ(rm+1)=(2π)mm+1canbeusedtoprove.

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