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arXiv · 1103.1585

Finite, closed-form expressions for the partition function and for Euler, Bernoulli, and Stirling numbers

Jerome Malenfant
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Abstract

We find general solutions to the generating-function equation sum c_q^{(X)} z^q = F(z)^X, where X is a complex number and F(z) is a convergent power series with |F(0)| >0. We then use these results to derive finite expressions containing only integers or simple fractions for partition functions and for Euler, Bernoulli, and Stirling numbers.

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Jerome Malenfant. 2011-05-24. Finite, closed-form expressions for the partition function and for Euler, Bernoulli, and Stirling numbers. https://arxiv.org/abs/1103.1585

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