Answer by A l'Maeaux for Proof that the series for the generating function of...
I figured it out with the help of Andrews' book The Theory of Partitions. Of course in hindsight, it seems easy.The sequence of partial sums$$S_N = \sum_{n=0}^N p(n) |q|^n$$is clearly increasing, and...
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For $|q| < 1$, the generating function of the partition function $p(n)$ is given by$$\sum_{n=0}^\infty p(n) q^n = \prod_{k=1}^\infty {1 \over 1-q^k}. \tag{1}$$I have an intuitive understanding of...
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