author = {Koustav Banerjee and Peter Paule and Cristian-Silviu Radu and Carsten Schneider},
title = {{Asymptotics for the reciprocal and shifted quotient of the partition function}},
language = {english},
abstract = { Let $p(n)$ denote the partition function. In this paper our main goal is to derive an asymptotic expansion up to order $N$ (for any fixed positive integer $N$) along with estimates for error bounds for the shifted quotient of the partition function, namely $p(n+k)/p(n)$ with $kin mathbb{N}$, which generalizes a result of Gomez, Males, and Rolen. In order to do so, we derive asymptotic expansions with error bounds for the shifted version $p(n+k)$ and the multiplicative inverse $1/p(n)$, which is of independent interest. },
number = {24-06},
year = {2024},
month = {December},
keywords = {{integer partitions, Hardy-Ramanujan Rademacher formula, asymptotic expansion, shifted quotient of partitions, symbolic summation},
length = {43},
license = {CC BY 4.0 International},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}