# To show two formal power series equal

I am wondering whether the following two formal power series are equal: $A(x)=\Pi_{k=1}^{\infty}\frac{1}{1-x^{2k-1}}$, $B(x)=\Pi_{k=1}^{\infty}(1+x^k)$.

• A and B are not series. – William Elliot Mar 4 '18 at 8:32
• @WilliamElliot: They are both series: $A(x)=\sum_{n=0}^\infty p(n|\text{parts all odd})x^n$ and $B(x)=\sum_{n=0}^\infty p(n|\text{parts distinct})x^n$. Here $p(n)$ is the number of partitions of $n$. – Markus Scheuer Mar 4 '18 at 8:37