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- W4296413564 abstract "Asymptotic study on the partition function $p(n)$ began with the work of Hardy and Ramanujan. Later Rademacher obtained a convergent series for $p(n)$ and an error bound was given by Lehmer. Despite having this, a full asymptotic expansion for $p(n)$ with an explicit error bound is not known. Recently O'Sullivan studied the asymptotic expansion of $p^{k}(n)$-partitions into $k$th powers, initiated by Wright, and consequently obtained an asymptotic expansion for $p(n)$ along with a concise description of the coefficients involved in the expansion but without any estimation of the error term. Here we consider a detailed and comprehensive analysis on an estimation of the error term obtained by truncating the asymptotic expansion for $p(n)$ at any positive integer $n$. This gives rise to an infinite family of inequalities for $p(n)$ which finally answers to a question proposed by Chen. Our error term estimation predominantly relies on applications of algorithmic methods from symbolic summation." @default.
- W4296413564 created "2022-09-20" @default.
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- W4296413564 date "2022-09-16" @default.
- W4296413564 modified "2023-09-24" @default.
- W4296413564 title "Error bounds for the asymptotic expansion of the partition function" @default.
- W4296413564 doi "https://doi.org/10.48550/arxiv.2209.07887" @default.
- W4296413564 hasPublicationYear "2022" @default.
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