11 citations · 12 across the 5 of their papers we have counts for
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On the Matrix-Element Expansion of a Circulant Determinant
Jerome Malenfant
The determinant of an circulant matrix ] can be expanded in the form det$ ~M= \sum C_{a_0 a_1 ...a_{N-1}} x_{a_0} x_{a_1}...x_{a…
Generalizing Ramanujan's J Functions
Jerome Malenfant
We generalize Ramanujan's expansions of the fractional-power Euler functions (q^{1/5})_{\infty} = [ J_1 - q^{1/5} + q^{2/5} J_2 ](q^5)_{\infty} and (q^{1/7})_{\infty} = [ J_1 + q^{…
A determinant formula for the partition function p(7k + a)
Jerome Malenfant
We derive expressions for the partition function p(n), with n in the form 7k+a, as (k+1)-dimensional determinants.
Factorization of and Determinant Expressions for the Hypersums of Powers of Integers
Jerome Malenfant
We derive a compact determinant formula for calculating and factorizing the hypersum polynomials S^{(L)}_k(N) \equiv \sum_{n_1=1}^N ...\sum_{n_{L+1}=1}^{n_{L}}(n_{L+1})^k expressed…
Finite, closed-form expressions for the partition function and for Euler, Bernoulli, and Stirling numbers
Jerome Malenfant
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…