Inequalities for higher order differences of the logarithm of the overpartition function and a problem of wang-xie-zhang

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SUMMARY

    A positive sequence {an }n≥0 is said to be log-concave (resp. log-convex) if for all n ≥ 1, a2n ≥ an-1 an+1 (resp. a2n ≤ an-1 an+1 ), and it is said to be strictly log-concave (resp. strictly log-convex) if the inequality is strict. A sequence {an }n≥k is called ratio log-convex if {an+1 /an }n≥k is log-convex or, equivalently, for n ≥ k + 1, 3 log an-1=log an+2 - 3 log an+1 + 3 log an - log an-1 ≥ 0, where be . . .

     

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