Explicit Representations of Meromorphic Functions as Quotients of Entire Functions Any meromorphic function can be expressed as a quotient of two entire functions. However many times meromorphic functions are not given as a quotient. Is there a general algorithm or method, given a meromorphic function (i.e. you know all the poles and their orders), to express it as a quotient of entire functions?
How does one even do it for the Weierstrass $\mathfrak{p}$ function? 

Use the method given in the proof of the Weierstrass Factorization theorem to construct a function $g$ with zeros at the poles of your function $f$. Then your desired quotient is $\displaystyle \frac{fg}{g}$.
