Newbetuts

Why does $ \frac{2x}{2+x}$ provide a particularly tight lower bound for $\ln(1+x)$ for small positive values of $x$?

Converse of Taylor's Theorem

Approximating smooth function on $[0,1]$ by Bernstein polynomial (interested in approximation rate in $L^2$ norm)

Does this "inverse Taylor series" exist in literature?

Function for which trapezoidal rule outperforms midpoint rule for every $n$

Approximating $\log x$ with roots

Why does the sup norm make the results of approximation theory independent from the unknown distribution of the input data?

Truncation error with growing step size

Proving that: $9.9998\lt \frac{\pi^9}{e^8}\lt 10$?

Advantage of Bernstein polynomial basis

What is a nice way to compute $f(x) = x / (\exp(x) - 1)$?

Multivariate Weierstrass theorem?

$f=\underset{+\infty}{\mathcal{O}}\bigr(f''\bigl)$ implies that $f=\underset{+\infty}{\mathcal{O}}\bigr(f'\bigl)$.

Weierstrass factorization of sine, and related questions

Is Ramanujan's approximation for the factorial optimal, or can it be tweaked? (answer below)

Uniform approximation by even polynomial

New posts in approximation-theory

Why can't the set of algebraic polynomials of degree at most k be dense in $C(\mathbb{R}^n)$

Approximation of ln(x) in the vicinity of x=0

Natural cubic spline interpolation error estimate

Why is the polynomial best approximation to an even function itself even?

Why does $ \frac{2x}{2+x}$ provide a particularly tight lower bound for $\ln(1+x)$ for small positive values of $x$?

Converse of Taylor's Theorem

Approximating smooth function on $[0,1]$ by Bernstein polynomial (interested in approximation rate in $L^2$ norm)

Does this "inverse Taylor series" exist in literature?

Function for which trapezoidal rule outperforms midpoint rule for every $n$

Approximating $\log x$ with roots

Why does the sup norm make the results of approximation theory independent from the unknown distribution of the input data?

Truncation error with growing step size

Proving that: $9.9998\lt \frac{\pi^9}{e^8}\lt 10$?

Advantage of Bernstein polynomial basis

What is a nice way to compute $f(x) = x / (\exp(x) - 1)$?

Multivariate Weierstrass theorem?

$f=\underset{+\infty}{\mathcal{O}}\bigr(f''\bigl)$ implies that $f=\underset{+\infty}{\mathcal{O}}\bigr(f'\bigl)$.

Weierstrass factorization of sine, and related questions

Is Ramanujan's approximation for the factorial optimal, or can it be tweaked? (answer below)

Uniform approximation by even polynomial