New inequalities for p(n) and $$\log p(n)$$

Autor: Koustav Banerjee, Peter Paule, Cristian-Silviu Radu, WenHuan Zeng
Rok vydání: 2022
Předmět:
Zdroj: The Ramanujan Journal.
ISSN: 1572-9303
1382-4090
DOI: 10.1007/s11139-022-00653-6
Popis: Let p(n) denote the number of partitions of n. A new infinite family of inequalities for p(n) is presented. This generalizes a result by William Chen et al. From this infinite family, another infinite family of inequalities for $$\log p(n)$$ log p ( n ) is derived. As an application of the latter family one, for instance obtains that for $$n\ge 120$$ n ≥ 120 , $$\begin{aligned} p(n)^2>\Biggl (1+\frac{\pi }{\sqrt{24}n^{3/2}}-\frac{1}{n^2}\Biggr )p(n-1)p(n+1). \end{aligned}$$ p ( n ) 2 > ( 1 + π 24 n 3 / 2 - 1 n 2 ) p ( n - 1 ) p ( n + 1 ) .
Databáze: OpenAIRE
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