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Level 5: The Rogers–Ramanujan Continued Fraction

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Ramanujan's Theta Functions

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Abstract

We prove that

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

and develop the rich properties of the infinite product.

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Authors and Affiliations

  1. Institute of Natural and Mathematical Science, Massey University, Auckland, New Zealand

    Shaun Cooper

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  1. Shaun Cooper
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Cooper, S. (2017). Level 5: The Rogers–Ramanujan Continued Fraction. In: Ramanujan's Theta Functions. Springer, Cham. https://doi.org/10.1007/978-3-319-56172-1_6

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