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I have Mathematica 11.0. I would like to see power series coefficients of a q-series (having q-Pochhammer symbols in the summands) together in order to look for certain arithmetic information.

Earlier, when I had Mathematica 9, I used to evaluate, say,

Series[Sum[q^(n^2 + n)/QPochhammer[q, q^2, n + 1], {n, 0, 10}], {q, 0, 10}]

to find the partial sum of this third order mock theta function $\nu(-q)$ up to $q^{10}$. And this used to work perfectly. However, now I just get an output consisting of expressions like

(1-QPochhammer^{(1, 0, 0)}[0, 0, 2] q^3

Could someone please tell me why this is happening in the newer version? I would also appreciate any alternate procedure for calculating the partial sums of a q-series written as a power series.

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  • $\begingroup$ Use FunctionExpand: Series[Sum[ q^(n^2 + n)/QPochhammer[q, q^2, n + 1] // FunctionExpand, {n, 0, 10}], {q, 0, 10}] $\endgroup$ – Bob Hanlon Feb 1 '18 at 2:38
  • $\begingroup$ An alternative to using FunctionExpand is to use Sum[q^(n^2 + n)/QPochhammer[q, q^2, n + 1], {n, 0, 10}] /. q -> q + O[q]^10 $\endgroup$ – Carl Woll Feb 1 '18 at 3:26
  • $\begingroup$ @CarlWoll - since the Series is to include q^10, the replacement should be q -> q + O[q]^11 $\endgroup$ – Bob Hanlon Feb 1 '18 at 4:01
  • $\begingroup$ Great. It worked! Thank you all so much! $\endgroup$ – adixit Feb 1 '18 at 6:02