Conditions must satisfy $f: (a, b) \to \mathbb{R}$ so that its Taylor series converge to f itself.
45517
Prove Taylor series converges to $f$.
146088
Proof or Counterexample on the Convergence of a Series
4956
Connection between Fourier transform and Taylor series
98371
Convergence of the $e^x$ Taylor series
53101
Is it true that the relation |A| < |B| is a sufficient condition for claiming that $f$ is a bijection?
1582
$f(x+1)-f(x)$ converges $\Rightarrow\frac{f(x)}x$ converges
117716
Condition on function $f:\mathbb{R}\rightarrow \mathbb{R}$ so that $(a,b)\mapsto | f(a) - f(b)|$ generates a metric on $\mathbb{R}$
30470
converge and converge absolutely of a series
67848
Let $A$ be the set of all functions $f:\mathbb{R}\to\mathbb{R}$ that satisfy the following two properties.
132018
problem involving series that converges depending on another series converging
34077
Let $f:\mathbb{R}\to\mathbb{R}$ satisfy $f\big(x-f(y)\big)=f\big(f(y)\big)+x\cdot f(y)+f(x)-1$ for all $x,y\in\mathbb{R}$.
144322
Prove for bounded $f$, if $f:[a,r] \to \mathbb{R}$ is Riemann-Integrable for $r \in [a,b)$ then $f:[a.b] \to \mathbb{R}$ is Riemann-Integrable
105497
A function satisfying a series equation
110415
Proving a sequence of step functions converges pointwise to a function $f$.
50012
$f: [a,b] \to \mathbb{R}$, $f(a) = f(b)$. Show $\exists c \in [a, \frac{a+b}{2} ]$ with $f(c)=f(c+\frac{b-a}{2})$
112767
Taylor Series type inequality
124562
$f:\mathbb{R}^n \to \mathbb{R}$ has expansion $\sum_i g_i(x)x^i$