Level 10: Ramanujan’s Function k

Shaun Cooper
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Shaun Cooper: Massey University, Institute of Natural and Mathematical Science

Chapter Chapter 10 in Ramanujan's Theta Functions, 2017, pp 523-551 from Springer

Abstract: Abstract We conduct a detailed analysis of Ramanujan’s function k = k(q) defined by k = q ∏ j = 1 ∞ ( 1 − q 10 j − 9 ) ( 1 − q 10 j − 8 ) ( 1 − q 10 j − 2 ) ( 1 − q 10 j − 1 ) ( 1 − q 10 j − 7 ) ( 1 − q 10 j − 6 ) ( 1 − q 10 j − 4 ) ( 1 − q 10 j − 3 ) $$k = q\prod _{j=1}^{\infty }\frac{(1 - q^{10j-9})(1 - q^{10j-8})(1 - q^{10j-2})(1 - q^{10j-1})} {(1 - q^{10j-7})(1 - q^{10j-6})(1 - q^{10j-4})(1 - q^{10j-3})}$$ and obtain results that are analogues of theorems in Chapters 5–9

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-56172-1_11

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DOI: 10.1007/978-3-319-56172-1_11

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