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Question: What are the $q$ power series with $\pm1$ coefficients?

This question arose when I saw this:

$\ldots$ Thus, we may write$$f(-q^{1/5})=\sum\limits_{n=-\infty}^{\infty}(-1)^nq^{n(3n+1)/10}=J_1+q^{2/5}J_2+q^{1/5}J_3\tag1$$ Where $J_1,J_2,J_3$ are power series in $q$ with coefficients $\pm1$.

I'm not too sure what they meant by "power series in $q$ with coefficients $\pm1$." I tried searching up "power series in $q$" on the Internet, and nothing popped up.

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    This is probably a good starting point: https://en.wikipedia.org/wiki/Q-analog – 2017-01-27
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    $\sum_{n=1}^{\infty} z^{n}/n$ is a power serie in $z$, $1+p+p^{2}$ is a polynomial in $p$, etc – 2017-01-27
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    "Power series in $q$" just means it's a power series in a variable, and that variable is $q$ as opposed to something else. "Coefficients $\pm 1$" means that the coefficients of that power series are either $1$ or $-1$. – 2017-01-27
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    See [this answer](http://math.stackexchange.com/a/1960205/276986) for a derivation of the "Fourier coefficients, $q$-expansion" of a modular form. The idea is that $g(q) = f(\frac{\log q}{2i\pi})$ is meromorphic on the unit disk, so it has a Laurent series $g(q) = \sum_n a_n q^n$ valid for $|q|$ small enough, and $f(\tau) = \sum_n a_n e^{2i \pi n \tau}$ has a Fourier expansion, valid for $Im(\tau)$ large enough – 2017-01-27

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