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THE LEVEL 12 ANALOGUE OF RAMANUJAN’S FUNCTION
$k$
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 101 / Issue 1 / August 2016
- Published online by Cambridge University Press:
- 22 January 2016, pp. 29-53
- Print publication:
- August 2016
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- Article
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- You have access
- Export citation
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We provide a comprehensive study of the function
$h=h(q)$ defined by and show that it has many properties that are analogues of corresponding results for Ramanujan’s function
$$\begin{eqnarray}h=q\mathop{\prod }_{j=1}^{\infty }\frac{(1-q^{12j-1})(1-q^{12j-11})}{(1-q^{12j-5})(1-q^{12j-7})}\end{eqnarray}$$
$k=k(q)$ defined by 
$$\begin{eqnarray}k=q\mathop{\prod }_{j=1}^{\infty }\frac{(1-q^{10j-1})(1-q^{10j-2})(1-q^{10j-8})(1-q^{10j-9})}{(1-q^{10j-3})(1-q^{10j-4})(1-q^{10j-6})(1-q^{10j-7})}.\end{eqnarray}$$
