Skip to content

Commit

Permalink
fix(taylor): typo, (p-R,P+R) instead of (-R,R)
Browse files Browse the repository at this point in the history
  • Loading branch information
vEnhance committed Apr 10, 2024
1 parent 5d295bc commit ae78d40
Showing 1 changed file with 2 additions and 2 deletions.
4 changes: 2 additions & 2 deletions tex/calculus/taylor.tex
Original file line number Diff line number Diff line change
Expand Up @@ -271,9 +271,9 @@ \section{Analytic functions}
\begin{itemize}
\ii the Taylor series of $f$ at $p$ has radius of convergence $R > 0$; \emph{and}
\ii that Taylor series actually does converge to the value $f(x)$
for every input $x \in (-R,R)$ within the radius of convergence.
for every input $x \in (p-R,p+R)$ within the radius of convergence.
\end{itemize}
Then $f$ is analytic on $(-R, R)$.
Then $f$ is analytic on $(p-R, p+R)$.
\label{prop:taylor_series_are_analytic}
\end{proposition}
This result is nontrivial because \emph{a priori} we only know $f$ is analytic at $p$;
Expand Down

0 comments on commit ae78d40

Please sign in to comment.