New posts in power-series

Find the sum: $\sum_{n=0}^\infty \frac{(n!)^2}{(2n)!}x^n$

real-analysis calculus sequences-and-series summation power-series

$\sum (-1)^n/n$ fails the p-series test, but passes the alternating series test?

real-analysis sequences-and-series power-series

Proving the sum of squares of sine and cosine using the Cauchy product formula

power-series binomial-coefficients cauchy-product

Sum of 1.5-powers of natural numbers

combinatorics power-series

Radius of Convergence of power series of Complex Analysis

sequences-and-series complex-analysis convergence-divergence power-series

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

prove that $(1 + x)^\frac{1}{b}$ is a formal power series

analysis power-series

Integral $\int_0^\frac{\pi}{2} \arcsin(\sqrt{\sin x}) dx$

integration power-series closed-form

Find the value $\binom {n}{0} + \binom{n}{4} + \binom{n}{8} + \cdots $, where $n$ is a positive integer.

summation power-series binomial-coefficients

Prove $\sum_{i=0}^n (-1)^{n-i} \binom{n+1}{i} (i+1)^n = (n+2)^n$

calculus sequences-and-series combinatorics summation power-series

Estimate $\displaystyle\int_0^\infty\frac{t^n}{n!}e^{-e^t}dt$ accurately.

asymptotics power-series gamma-function

Calculate the closed form of $\frac{\sqrt[5]{5}}{\sqrt[3]{3}}\cdot \frac{\sqrt[9]{9}}{\sqrt[7]{7}}\cdot \frac{\sqrt[13]{13}}{\sqrt[11]{11}}\cdot ...$

calculus power-series

Radius of convergence of the complex serie $(z-i)^n/n!$

sequences-and-series complex-analysis power-series

Formal power series with coefficient in $\{0,1 \}$ which is not rational

abstract-algebra power-series

$\sin^2(x)+\cos^2(x) = 1$ using power series

calculus trigonometry power-series

Why the radius of convergence and not "areas of convergence" for power series?

calculus real-analysis power-series

For which values of x does the power series converge or diverge?

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

How to prove a polynomial can be written as Taylor-style?

calculus real-analysis derivatives power-series taylor-expansion

Challenging probability problem

probability sequences-and-series power-series roots

Lagrange inversion theorem and Legendre polynomials generating function

real-analysis complex-analysis power-series lagrange-inversion