http://dlmf.nist.gov/17.5#17.5.5 (or BHS (II.5)) gives [image: \, _1\phi _1\left(a;c;q,\frac{c}{a}\right)=\frac{\left(\frac{c}{a};q\right)_{\infty }}{(c;q)_{\infty }}] for |q|<1. This has the peculiar special case [image: \, _1\phi _1(q;q z;q,z)=1-z] independent of q. But this can be generalized to |q|≠1: [image: \, _1\phi _1(q;q z;q,z)=\frac{z}{\left(\frac{1}{q z};\frac{1}{q}\right)_{\infty }}-z+1] Can we similarly generalize BHS (II.5)? Maybe not. E.g., [image: \, _1\phi _1\left(q^2;c q^2;q,c\right)=(c-1) (c q-1) \left(\frac{c+q-c q}{c (q-1) \left(\frac{1}{c};\frac{1}{q}\right)_{\infty }}+1\right)] We seem to be off to a rough start. I just implemented the base reciprocation formula for general rφs, which I was surprised BHS and DLMF 17.5 omit. Now I'm less surprised--it's a typesetting challenge. --rwg If instead of typesetting you see the alternate text, e.g., [image: \, _1\phi _1(q;q z;q,z)=\frac{z}{\left(\frac{1}{q z};\frac{1}{q}\right)_{\infty }}-z+1] Then paste \, _1\phi _1(q;q z;q,z)=\frac{z}{\left(\frac{1}{q z};\frac{1}{q}\right)_{\infty }}-z+1 into the window at www.texify.com . (Thanks, Neil!)