2 results
THE LEVEL 12 ANALOGUE OF RAMANUJAN’S FUNCTION
$k$
- Part of
-
- 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
-
- Article
-
- You have access
- Export citation
-
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 
$$\begin{eqnarray}k=q\mathop{\prod }_{j=1}^{\infty }\frac{(1-q^{10j-1})(1-q^{10j-2})(1-q^{10j-8})(1-q^{10j-9})}{(1-q^{10j-3})(1-q^{10j-4})(1-q^{10j-6})(1-q^{10j-7})}.\end{eqnarray}$$
On generalized complete elliptic integrals and modular functions
- Part of
-
- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 55 / Issue 3 / October 2012
- Published online by Cambridge University Press:
- 12 April 2012, pp. 591-611
-
- Article
-
- You have access
- Export citation
