Lambda Hypergeometric Function

$\begin{displaymath} \lambda(t)=16 q\prod_{n=1}^\infty \left({1+q^{2n}\over 1+q^{2n-1}}\right)^8, \end{displaymath}$

(1)

where

is the Nome. The lambda hypergeometric functions satisfy the recurrence relationships

$\displaystyle \lambda(t+2)$	$\textstyle =$	$\displaystyle \lambda(t)$	(2)
$\displaystyle \lambda\left({t\over 2t+1}\right)$	$\textstyle =$	$\displaystyle \lambda(t).$	(3)