An explicit series for the tetration of a complex height

[JmsNxn]

Thanks for your elaboration. I think it is supposed to be \( q^{\binom {n-m} 2} \) rather than \( q^{\binom n 2} \) in the first formula (the definition of \( F(z) \)). Here is a link to my Mathematica program that uses the proposed formula to numerically calculate tetration values: http://goo.gl/03L8dV

Yes, you're right. Just a typo .