Question about power series - Printable Version +- Tetration Forum (https://math.eretrandre.org/tetrationforum) +-- Forum: Tetration and Related Topics (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1) +--- Forum: Mathematical and General Discussion (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=3) +--- Thread: Question about power series (/showthread.php?tid=266) Question about power series - tommy1729 - 04/05/2009 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 ) RE: weird question - andydude - 04/06/2009 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.