I want to define the product of n complex functions:

B(z)=\displaystyle\prod_{k=1}^n\frac{z-p_k}{1-\overline{p}_kz}, where p_k are n complex numbers of modulus <1.

I calculated a vector of partial products, and the function B is the last one in the respective vector.

Is there a simpler way to get the definition of this product?

```
function fproduct(f, g)
z -> f(z) * g(z)
end
BlaschkeF(z::Complex; p=0.5+0*im) = (z-p)/(1-conj(p)*z)
unitf(z::Complex) = 1.0+0*im
n=5
params = [0.95*cis(k*2pi/n) for k in 0:n-1]
prodf = Function[]
for p in params
g = z->BlaschkeF(z;p=p)
if !isempty(prodf)
ppr = fproduct(last(prodf), g) #ppr -partial product
else
ppr = fproduct(unitf, g)
end
push!(prodf, ppr)
end
B(z)=last(prodf)(z)
```