Basic hypergeometric series

Series[(1 - q)^(-1), {q, 0, 40}]
Series[\!\(<br> \*UnderoverscriptBox[\(\[Product]\), \(k = 1\), \(100\)]\((1 -<br>     q^k)\)\), {q, 0, 100}]
h[q_] := 1 - q - q^2 + q^5 + q^7 - q^12 - q^15 + q^22 + q^26 - q^35 -
  q^40 + q^51 + q^57 - q^70 - q^77 + q^92 + q^100
f[q_] := \!\(<br> \*UnderoverscriptBox[\(\[Sum]\), \(k = 0\), \(100\)]\(PartitionsP[<br>     k] q^k\)\)
d[n_] := DivisorSigma[1, n]
g[q_] := \!\(<br> \*UnderoverscriptBox[\(\[Sum]\), \(k = 1\), \(100\)]\(d[k] q^k\)\)
Expand[f[q]*h[q]]
Expand[g[q]*h[q]]