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Level 10: Ramanujan’s Function k

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Ramanujan's Theta Functions

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Abstract

We conduct a detailed analysis of Ramanujan’s function k = k(q) defined by

$$k = q\prod _{j=1}^{\infty }\frac{(1 - q^{10j-9})(1 - q^{10j-8})(1 - q^{10j-2})(1 - q^{10j-1})} {(1 - q^{10j-7})(1 - q^{10j-6})(1 - q^{10j-4})(1 - q^{10j-3})}$$

and obtain results that are analogues of theorems in Chapters 5–9

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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 10: Ramanujan’s Function k . In: Ramanujan's Theta Functions. Springer, Cham. https://doi.org/10.1007/978-3-319-56172-1_11

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