[math-fun] q^9 in a theta constant

https://en.wikipedia.org/wiki/Dedekind_eta_function gives a peculiar theta expression for Dedekind eta. Combining with the more obvious DedekindEta[\[Tau]] -> EllipticTheta[1, Pi/3, E^((I Pi \[Tau])/3)]/Sqrt[3] gives the weird-looking EllipticTheta[1,Pi/3, q] == -Sqrt[3] q^(25/4) EllipticTheta[4, 15/2 I Log[q], q^9] == (Sqrt[Pi/3] EllipticTheta[1, Pi/3, E^(Pi^2/(9 Log[q]))])/Sqrt[-Log[q]] (The latter via Jacobi's imaginary transformation.) --rwg