New posts in taylor-expansion

Weighted uniform convergence of Taylor series of exponential function

real-analysis sequences-and-series taylor-expansion uniform-convergence

What's the Maclaurin series for $\arcsin(x)$?

trigonometry taylor-expansion

Interesting limit: $I(n)=\lim_{x \to 0} (e^x-1)^{-n} - \left(\frac{x}{1!}+\frac {x^2}{2!}+\dotsb+\frac{x^n}{n!}\right)^{-n}$

calculus limits taylor-expansion

An issue with approximations of a recurrence sequence

complex-analysis asymptotics recurrence-relations dynamical-systems taylor-expansion

If $f''(x_0)$ exists then $\lim_{x \to x_0} \frac{f(x_0+h)-2f(x_0)+f(x_0-h)}{h^2} = f''(x_0)$

real-analysis derivatives taylor-expansion

$f^{(3)}(x) h$ was sucked in big O

real-analysis asymptotics taylor-expansion

Can $ I_n(z) = (\frac{z}{2})^n\sum_{k=0}^\infty\frac{(-1)^k}{k!(n+k)!}\frac{1}{k+(n+k)+1}(\frac{z}{2})^{2k}$ be expressed by the Bessel function?

taylor-expansion bessel-functions

By using a geometric series and a factorisation, compute the first three terms of this given Taylor expansion

calculus real-analysis taylor-expansion

Taylor expansion of a function of a symmetric matrix

linear-algebra matrices taylor-expansion matrix-calculus

Bound on remainder for vector valued Taylor series

real-analysis multivariable-calculus taylor-expansion

Why do un-integrable functions exist?

integration taylor-expansion elementary-functions

Confusion about the expecation of infinite summations

sequences-and-series convergence-divergence taylor-expansion expected-value

Closed-forms of infinite series with factorial in the denominator

calculus sequences-and-series taylor-expansion factorial closed-form

proof that Even powers of an odd function's taylor polynomial vanish

calculus taylor-expansion

How do I evaluate $\sum_{n=1}^{\infty}\frac{(-1)^{n+1}H_n}{2n+1}?$

calculus sequences-and-series taylor-expansion harmonic-numbers catalans-constant

If $f^2$ and $f^3$ are $C^{\infty}(\mathbb R)$ then $f$ is $C^{\infty}(\mathbb R)$

real-analysis derivatives taylor-expansion

Taylor series for different points... how do they look?

analysis power-series taylor-expansion

Convergence of the quadratic map $\left(x-\left(x-\left(x- \dots \right)^2 \right)^2 \right)^2$?

recurrence-relations taylor-expansion quadratics newton-raphson bifurcation

Clever derivation of $\arcsin(x)$ Taylor series

calculus taylor-expansion

Taylor expansion of $\sin \pi z$ at $z = -1$.

trigonometry taylor-expansion