User blog comment:King2218/The Theta Function/@comment-5150073-20140325134424/@comment-5150073-20140325135702

Not so easy, for example, you don't even know how to get $$\theta(\omega,1)$$ from $$\theta(\omega,0)$$. I would say that $$\theta(\omega,1)[n] = \theta(n,\theta(\omega,0)+1)$$, but it looks too clunky compared to definitions in $$\psi$$.