Question about power series

[tommy1729]

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 )

[andydude]

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.