New posts in power-series

Power series of $\frac{x+1}{x^2+5}$

real-analysis calculus power-series

About the inequality $\left(\ln\left(\frac{4+x}{2x+2}\right)\right)^{2}\leq x!$

inequality logarithms power-series gamma-function

Proving $\pi=(27S-36)/(8\sqrt{3})$, where $S=\sum_{n=0}^\infty\frac{\left(\left\lfloor\frac{n}{2}\right\rfloor!\right)^2}{n!}$ [closed]

calculus sequences-and-series summation power-series pi

Do you have equipment with the computational accuracy to test my infinite series representation for Gamma(m), or (m-1)! ….?

power-series gamma-function

Laurent Series of $f(z) = \frac{(z+1)^2}{z(z^3+1)}$ about $z = 0$?

sequences-and-series complex-analysis power-series laurent-series

Let $f$ be an analytic isomorphism on the unit disc $D$, find the area of $f(D)$

complex-analysis power-series

Determine if this series converges or diverges

calculus sequences-and-series power-series

Simplifying $\cosh x + \sinh x$, $\cosh^2 x + \sinh^2 x$, $\cosh^2 x - \sinh^2 x$ using only the Taylor Series of $\cosh,\sinh$

calculus power-series taylor-expansion

How to prove that the exponential function is the inverse of the natural logarithm by power series definition alone

power-series

Why doesn't the Stone-Weierstrass theorem imply that every function has a power series expansion?

real-analysis power-series calculus

Do the Taylor series of $\sin x$ and $\cos x$ depend on the identity $\sin^2 x + \cos^2 x =1$?

combinatorics trigonometry power-series taylor-expansion

Why does the taylor series of $\ln (1 + x)$ only approximate it for $-1<x \le 1$?

calculus sequences-and-series power-series

Uniform convergence in the endpoints of an interval

real-analysis power-series uniform-convergence

Any intuitive answer to the summation of power of 2? [duplicate]

summation power-series

Radius of convergence of power series

reference-request complex-analysis power-series

What kind of functions cannot be described by the Taylor series? Why is this?

power-series taylor-expansion elementary-functions

Maclaurin series of $(1+x^3)/(1+x^2)$

sequences-and-series power-series taylor-expansion

Suppose $\sum_{i = 1} a_i \sum_{i = 1} b_i < \infty$. If $\sum_{i = 1} a_i = \infty$, what does it say about $(b_i)$?

sequences-and-series summation power-series infinity

Are Taylor series and power series the same "thing"?

real-analysis complex-analysis power-series taylor-expansion

Math contest: Find number of roots of $F(x)=\frac{n}{2}$ involving a strange integral.

calculus integration power-series contest-math