New posts in power-series

Asymptotic equivalent of $\sum_{n\ge0} q^{n^2}{x^n}$ as $x\to+\infty$

How to find the radius of convergence?

Third degree Taylor series of $f(x) = e^x \cos{x} $

Closed form of $\sum_{n = 1}^{\infty} \frac{n^{n - k}}{e^{n} \cdot n!}$

Solution of $y''+xy=0$

Convergence of the $e^x$ Taylor series

How to compute the coefficients of this generating function

Identify infinite sum: $\sum\limits_{n=0}^{+\infty}\frac{x^{4n}}{(4n)!}$

Calculation of limit without stirling approximation

Intuitive explanation of proof of Abel's limit theorem

Closed form solution method for infinite sum (but not "by inspection")

Prime consequences [closed]

Finding the power series of $\arcsin x$

What is the fraction field of $R[[x]]$, the power series over some integral domain?

How do I express the sum $(1+k)+(1+k)^2+\ldots+(1+k)^N$ for $|k|\ll1$ as a series?

Series of nested integrals

What is the Riemann surface of $y=\sqrt{z+z^2+z^4+\cdots +z^{2^n}+\cdots}$?

How to prove convergence of polynomials in $e$ (Euler's number)

Why $e^{\pi}-\pi \approx 20$, and $e^{2\pi}-24 \approx 2^9$?

Proving that $\lim_{x\to1^-}\left(\sqrt[a]{1-x}\cdot\sum_{n=0}^\infty~x^{n^a}\right)=\Gamma\left(1+\frac1a\right)$