\[\varphi_{m,n}\left(z,q\right)=\varphi_{m,1}\left(z,q\right)\varphi_{1,n}\left(%
z,q\right)=\frac{1}{\varphi_{n,m}\left(z,q\right)}=\frac{\varphi_{m,1}\left(z,%
q\right)}{\varphi_{n,1}\left(z,q\right)}=\frac{\varphi_{1,n}\left(z,q\right)}{%
\varphi_{1,m}\left(z,q\right)}.\]