https://www.open.wolframcloud.com/objects/92e4170d-590a-4f41-91af-595a443c65... gives a nondescript nested radical times 𝚪(1/4)/π^¾, and then rewrites the radical as a product of binomial surds. Expanding the 𝜗 gives a really fast series for 𝚪(1/4)/π^¾. I'm unsure whether 𝜗s of yet higher powers of 𝕖^-π can be put in the binomial surds form. (Even if they can, they might burgeon infelicitously.) Also note Mathematica's bizarre insistence on writing the radical as reciprocal(√(reciprocal)) instead of just √. (This annoyed the heck of of Corey while he was writing his denester.) —rwg (And I have no idea how long these Cloud bits stick around.)