About the Project
5 Gamma FunctionProperties

§5.8 Infinite Products

5.8.1 Γ(z)=limkk!kzz(z+1)(z+k),
z0,1,2,,
5.8.2 1Γ(z)=zeγzk=1(1+zk)ez/k,
5.8.3 |Γ(x)Γ(x+iy)|2=k=0(1+y2(x+k)2),
x0,1,.

If

5.8.4 k=1mak=k=1mbk,

then

5.8.5 k=0(a1+k)(a2+k)(am+k)(b1+k)(b2+k)(bm+k)=Γ(b1)Γ(b2)Γ(bm)Γ(a1)Γ(a2)Γ(am),

provided that none of the bk is zero or a negative integer.