Partition functionHardy-Ramanujan-Rademacher formulaLet \\(\\hat{\\mathscr {L}}\\) be the operator given by \\(\\hat{\\mathscr {L}} \\{a_n\\}_{n \\ge 0} = \\{a_{n+1}^2 - a_{n} a_{n+2} \\}_{n \\ge 0}\\). A seque
This work was supported by the National Science Foundation of China. Rights and permissions Reprints and permissions About this article Cite this article Hou, QH., Zhang, ZR. r-log-concavity of partition functions. Ramanujan J 48, 117–129 (2019). https://doi.org/10.1007/s11139-017-9975-...
Partition functionHardy-Ramanujan-Rademacher formulaLet be the operator given by . A sequence is called asymptotically r-log-concave if are non-negative sequences for and some integer N. Let p(n) be the number of integer partitions of n. We prove that the sequence is asymptotically r-log-...
We deal with both some basic extensions like, for instance, the strong log-concavity and a more intriguing challenge that is the r-log-concavity of both quasi-polynomial-like functions in general, and the restricted partition function in particular. For each of the problems, we ...