Abstract
In 2009, Bringmann, Lovejoy and Osburn defined two analogues of the crank function for overpartitions, namely the first residual crank and second residual crank. For a positive integer [Formula: see text], we introduce the notion of a [Formula: see text]th residual crank function for overpartitions, examine the positive moments of these generalized crank functions while varying [Formula: see text], and prove some inequalities.
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