New posts in taylor-expansion

Which positive continuous functions satisfy $F(x) = F(e^x)-F(e^{-x})$ for $x\geq 0$?

sequences-and-series stochastic-processes taylor-expansion functional-equations

Asymptotics of the sum $\sum_{n=1}^\infty \frac{x^n}{n^n}$

sequences-and-series summation asymptotics taylor-expansion

What uniquely characterizes the germ of a smooth function?

calculus real-analysis taylor-expansion analyticity analytic-functions

Maclaurin expansion of $\arctan(x)/(1 − x).$

real-analysis calculus sequences-and-series analysis taylor-expansion

Summation Formula for Tangent/Secant Numbers

calculus trigonometry taylor-expansion generating-functions continued-fractions

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

logarithms taylor-expansion approximation approximation-theory

Taylor series not converging, other example than $\exp(-1/x^2)$?

calculus real-analysis convergence-divergence taylor-expansion

How do we know the Taylor expansion for $e^x$ works for all $x$? Or that it's analytic?

calculus sequences-and-series taylor-expansion exponential-function analytic-functions

Laurent expansion for sin(1/z)

complex-analysis taylor-expansion laurent-series

taylor's formula in $\mathbb{R}^n$ as exponential of derivative operator

calculus multivariable-calculus taylor-expansion

Find the 8th derivative of the function $h(x) = xe^x $using sequences

sequences-and-series derivatives taylor-expansion

Converse of Taylor's Theorem

real-analysis numerical-methods taylor-expansion functional-equations approximation-theory

Expansion of two Gamma function

taylor-expansion gamma-function

How do we know Taylor's Series works with complex numbers?

sequences-and-series complex-analysis trigonometry taylor-expansion

Lower bound on $\int_0^{\pi/4}\sin(\tan x)dx$

integration definite-integrals taylor-expansion

Quick way to expand $\cos^{-1}(\cos^2 x)$ up to $O(x^2)$

calculus taylor-expansion

Behaviour of function defined by Taylor series

calculus taylor-expansion

Finding Taylor's series of the function: $\frac{e^{a \sin^{-1}x}}{\sqrt{1-x^2}}$

real-analysis sequences-and-series power-series taylor-expansion

Taylor series of a polynomial

linear-algebra polynomials taylor-expansion

How do I use the Taylor series to calculate $\ln(4)$ with an error of $10^{-5}$ with no calculator?

derivatives taylor-expansion