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Inequalities for higher order differences of the logarithm of the overpartition function and a problem of Wang-Xie-Zhang

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Let p ¯ ( n ) denote the overpartition function. In this paper, our primary goal is to study the asymptotic behavior of the finite differences of the logarithm of the overpartition function, i.e., ( - 1 ) r - 1 Δ r log p ¯ ( n ) , by stu... ...