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Some product-to-sum identities. (English) Zbl 1282.11039

Summary: In this paper the infinite products
\[ \prod_{n=1}^\infty (1 + \sqrt{2}q^n +q^{2n} )^{2}, \quad \prod_{n=1}^\infty (1 + \sqrt{3}q^n +q^{2n} )^{3} \]
and
\[ \prod_{n=1}^\infty (1 + \frac{(1 + \sqrt{3})}{2}q^n +q^{2n} )^{5} \]
are determined.

MSC:

11F27 Theta series; Weil representation; theta correspondences
33E05 Elliptic functions and integrals
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