Finite, closed-form expressions for the partition function and for Euler, Bernoulli, and Stirling numbers
Number Theory
2011-05-25 v6
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.
Cite
@article{arxiv.1103.1585,
title = {Finite, closed-form expressions for the partition function and for Euler, Bernoulli, and Stirling numbers},
author = {Jerome Malenfant},
journal= {arXiv preprint arXiv:1103.1585},
year = {2011}
}
Comments
19 pages