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Level 8: The Ramanujan–Göllnitz–Gordon Continued Fraction

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Ramanujan's Theta Functions

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Abstract

We prove that

$$\displaystyle{ \frac{q^{1/2}} {1 + q + \frac{q^{2}} {1 + q^{3} + \frac{q^{4}} {1 + q^{5} + \frac{q^{6}} {1 + q^{7} + \cdots }}}} = q^{1/2}\prod _{ j=1}^{\infty }\frac{(1 - q^{8j-7})(1 - q^{8j-1})} {(1 - q^{8j-5})(1 - q^{8j-3})}}$$

and obtain results that are analogues of theorems in Chapters 5, 6, and 7.

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    Shaun Cooper

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Cooper, S. (2017). Level 8: The Ramanujan–Göllnitz–Gordon Continued Fraction. In: Ramanujan's Theta Functions. Springer, Cham. https://doi.org/10.1007/978-3-319-56172-1_9

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