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

Mathematics – Number Theory

Scientific paper

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19 pages

Scientific paper

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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