Level 9

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

Chapter Chapter 9 in Ramanujan's Theta Functions, 2017, pp 509-522 from Springer

Abstract: Abstract The identities η 1 3 η 9 3 + 9 + 27 η 9 3 η 1 3 = η 3 12 η 1 6 η 9 6 $$ \frac{\eta _{1}^{3}} {\eta _{9}^{3}} + 9 + 27\frac{\eta _{9}^{3}} {\eta _{1}^{3}} = \frac{\eta _{3}^{12}} {\eta _{1}^{6}\eta _{9}^{6}} $$ and 1 8 9 P ( q 9 ) − P ( q ) = η 3 10 η 1 3 η 9 3 $$ \frac{1} {8}\left (9P(q^{9}) - P(q)\right ) = \frac{\eta _{3}^{10}} {\eta _{1}^{3}\eta _{9}^{3}} $$ are used to obtain results that are analogues of theorems in Chapters 5–8

Keywords: Ramanujan's Notebooks; Garven; Yesilyurt; Borwein; Eisenstein Series (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-56172-1_10

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DOI: 10.1007/978-3-319-56172-1_10

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