# Tetration Forum

Full Version: Question about power series
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ok , i have this weird question.

i encountered it when thinking about tetration , how exactly is complicated ...

do we have a typical series expansion for f(z) which always converges for R(z) and I(z) >= 0 ?

( where the infinite sum is considered as the limit of the averages , this limit always exists with that series expansion for R(z) and I(z) >= 0 )
tommy1729 Wrote:do we have a typical series expansion for f(z) which always converges for R(z) and I(z) >= 0 ?

Nope. We have a series expansion for ${}^{z}e$ about z=0 which seems to converge (no proof) where $|z|<2$ whose coefficients (not exact) can be approximated with several methods.