Finite differences of the logarithm of the partition function

DOI10.1090/mcom/2999zbMath1401.11134arXiv1407.0177OpenAlexW2964312531MaRDI QIDQ2792343

Larry X. W. Wang, Gary Y. B. Xie, William Y. C. Chen

Publication date: 9 March 2016

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.0177

zbMATH Keywords

upper boundspartition functiondifference operator

Mathematics Subject Classification ID

Bernoulli and Euler numbers and polynomials (11B68) Combinatorial inequalities (05A20) Analytic theory of partitions (11P82)

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Cites Work

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• Maximal multiplicative properties of partitions
• Log-concavity of the partition function
• Exact asymptotic formulas for the coefficients of nonmodular functions
• On the Lambert \(w\) function
• Differences of the partition function
• Asymptotic behavior of high‐order differences of the partition function
• On the differences of the partition function
• Finite Differences of the Partition Function
• Asymptotic expansions and inequalities for hypergeometric function
• Bounds for modified Bessel functions of the first and second kinds
• Partition Asymptotics from Recursion Equations
• A Convergent Series for the Partition Function p ( n )
• On the Series for the Partition Function