New posts in power-series

Bernoulli Numbers and Tangent numbers.

sequences-and-series combinatorics permutations power-series generating-functions

Evaluate this power series

calculus real-analysis power-series

Derive an explicit formula for a power series $\sum_{n=1}^\infty n^2x^n$

calculus sequences-and-series power-series

What is the difference between the Taylor and Maclaurin series?

sequences-and-series power-series taylor-expansion

Two different expansions of $\frac{z}{1-z}$

real-analysis sequences-and-series complex-analysis analysis power-series

Ramanujan's approximation for $\pi$

calculus power-series approximation pi

Formal power series coefficient multiplication

generating-functions power-series

Prove $\alpha \in R[[x]]$ is a unit iff $a_0 \in R$ is a unit

abstract-algebra ring-theory power-series

Sum of the form $r+r^2+r^4+\dots+r^{2^k} = \sum_{i=1}^k r^{2^i}$

summation power-series

Radius of Convergence - $\sum_{n=1}^{\infty}2^n x^{n^2}$

calculus sequences-and-series convergence-divergence power-series

Compute the radius of convergence of the power series $\sum_{n=0}^{\infty} n!x^n$

power-series

What does it mean intuitively for a Taylor Series to be centered at a specific point?

power-series taylor-expansion

Power series representation of arctangent: fails to converge everywhere

calculus power-series

If $a_0\in R$ is a unit, then $\sum_{k=0}^{\infty}a_k x^k$ is a unit in $R[[x]]$

ring-theory power-series

Can a Power Series tell when to stop?

complex-analysis soft-question power-series

Simplifying $\sum_{n=1}^{\infty}\frac{n\alpha^n}{(n-m)!(n+z)}(x-c)^{n-m}$

integration sequences-and-series definite-integrals power-series

On calculating $\int_0^1\ln(1-x^2)\;{\mathrm dx}$ -- where is the mistake?

analysis sequences-and-series integration power-series

How prove there is no continuous functions $f:[0,1]\to \mathbb R$, such that $f(x)+f(x^2)=x$.

calculus analysis continuity power-series functional-equations

How to calculate $f(x)$ in $f(f(x)) = e^x$?

power-series functional-equations tetration

Sum of Squares of Harmonic Numbers

combinatorics summation power-series harmonic-numbers