Pentagonal number theorem

In mathematics, Euler's pentagonal number theorem relates the product and series representations of the Euler function. It states that ∏ n = 1 ∞ ( 1 − x n ) = ∑ k = − ∞ ∞ ( − 1 ) k x k ( 3 k − 1 ) / 2 = 1 + ∑ k = 1 ∞ ( − 1 ) k ( x k ( 3 k + 1 ) / 2 + x k ( 3 k − 1 ) / 2 ) .