This dissertation develops and formalizes a polynomial variation of Meinardus' Theorem which is used to approximate a large class of polynomials generated by certain generating functions P(z, q) when z ∈ D.;Following the outline of the original Meinardus' Theorem, we begin by defining assumptions by which we can approximate P( z, q) using the analytic properties of the Cahen-Mellin integral. We then apply a variant of the circle method which exploits the use of Farey series to prove our main results.;The second part of the dissertation focuses on examples to which our theorem can be applied. We detail some examples of polynomial families to which can be approximated by our main theorem both of which are related to asymptotic enumeration of integer partitions.
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