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New posts in power-series
Asymptotic equivalent of $\sum_{n\ge0} q^{n^2}{x^n}$ as $x\to+\infty$
sequences-and-series
analysis
asymptotics
power-series
theta-functions
How to find the radius of convergence?
sequences-and-series
complex-analysis
analysis
convergence-divergence
power-series
Third degree Taylor series of $f(x) = e^x \cos{x} $
real-analysis
sequences-and-series
power-series
taylor-expansion
Closed form of $\sum_{n = 1}^{\infty} \frac{n^{n - k}}{e^{n} \cdot n!}$
lambert-w
sequences-and-series
summation
power-series
Solution of $y''+xy=0$
ordinary-differential-equations
power-series
Convergence of the $e^x$ Taylor series
sequences-and-series
power-series
How to compute the coefficients of this generating function
sequences-and-series
combinatorics
power-series
generating-functions
Identify infinite sum: $\sum\limits_{n=0}^{+\infty}\frac{x^{4n}}{(4n)!}$
sequences-and-series
power-series
Calculation of limit without stirling approximation
sequences-and-series
limits
power-series
Intuitive explanation of proof of Abel's limit theorem
convergence-divergence
power-series
intuition
uniform-convergence
Closed form solution method for infinite sum (but not "by inspection")
sequences-and-series
power-series
Prime consequences [closed]
sequences-and-series
prime-numbers
power-series
exponential-function
Finding the power series of $\arcsin x$
calculus
power-series
What is the fraction field of $R[[x]]$, the power series over some integral domain?
commutative-algebra
power-series
integral-domain
How do I express the sum $(1+k)+(1+k)^2+\ldots+(1+k)^N$ for $|k|\ll1$ as a series?
summation
power-series
Series of nested integrals
integration
power-series
integral-transforms
What is the Riemann surface of $y=\sqrt{z+z^2+z^4+\cdots +z^{2^n}+\cdots}$?
complex-analysis
power-series
riemann-surfaces
analyticity
How to prove convergence of polynomials in $e$ (Euler's number)
sequences-and-series
convergence-divergence
power-series
proof-writing
Why $e^{\pi}-\pi \approx 20$, and $e^{2\pi}-24 \approx 2^9$?
power-series
approximation
pi
laurent-series
q-series
Proving that $\lim_{x\to1^-}\left(\sqrt[a]{1-x}\cdot\sum_{n=0}^\infty~x^{n^a}\right)=\Gamma\left(1+\frac1a\right)$
calculus
sequences-and-series
limits
power-series
gamma-function
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