3
votes
1answer
268 views

Converse of the taylor's theorem in Banach Spaces

I would like to known if the following converse of the taylor's theorem is true: Let $E$, $F$ Banach spaces, and $f:E\rightarrow F$ continuous. Suppose there are $k$ continuous functions $T_i: E ...
28
votes
3answers
3k views

Is there an “elegant” non-recursive formula for these coefficients? Also, how can one get proofs of these patterns?

Hi. Not sure if this is a "good" question for this forum or if it'll get panned, but here goes anyway... Consider this problem. I've been trying to find a formula to expand the "regular iteration" ...