Abstract
Partial fractions arise again and again in the Lost Notebook. Indeed, we have already seen instances of partial fractions (e.g. [32, p. 271]) that specialize to mock theta functions. On pages 2 and 17 in his Lost Notebook [232], Ramanujan recorded four identities involving the rank generating function. Of course, Ramanujan would not have used this terminology, because the rank of a partition was not defined until 1944 by F.J. Dyson [130]. He defined the rank of a partition to be the largest part minus the number of parts.
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