entire functions approximation by orthogonal polynomials $P_{2n}(z) $

Question

let be an entire function with a taylor expansion valid on the whole complex plane

$ f(z)= \sum_{n=0}^{\infty} (-1)^{n}a_{n} z^{n} $

and the coefficients are ALL positive

my question is if there are examples so the ENTIRE function $ f(x)$ can be approximated by an orthogoanl polynomial in the following way

$ \frac{f(z)}{f(0)}= \frac{p_{2n}(z)}{p_{2n}}(0)$