Koustav Banerjee, Peter Paule, Silviu Radu, Carsten Schneider,
"Asymptotics for the reciprocal and shifted quotient of the partition function"
, Serie RISC Report Series, Johannes Kepler University Linz, Nummer 24-06, RISC, JKU, Hagenberg, Linz, 12-2024, ISSN: 2791-4267
Original Titel:
Asymptotics for the reciprocal and shifted quotient of the partition function
Sprache des Titels:
Englisch
Original Kurzfassung:
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.
Sprache der Kurzfassung:
Englisch
Veröffentlicher:
RISC, JKU
Verlagsanschrift:
Hagenberg, Linz
Serie:
RISC Report Series, Johannes Kepler University Linz
Forschungs-