New posts in power-series

Does this "inverse Taylor series" exist in literature?

reference-request power-series taylor-expansion approximation-theory

Find $\frac{1}{1.2.3.4}+\frac{4}{3.4.5.6}+\frac{9}{5.6.7.8}+\frac{16}{7.8.9.10}+\dots$

sequences-and-series power-series

Taylor series (or equivalent at $\epsilon\to0$) of the integral over $x$ of a function of $x$ and $\epsilon$

real-analysis integration power-series taylor-expansion

Ramanujan's Master Theorem relation to Analytic Continuation

integration complex-analysis power-series improper-integrals

Challenging integral $\int_{0}^{1}\frac{x\operatorname{li}(x)}{x^2+1}dx$

definite-integrals logarithms power-series improper-integrals

Suppose $ \sum a_k x^k $ uniformly converges at $ [0,R) $, then it converges pointwise at $ R $.

convergence-divergence power-series uniform-convergence

Proof of $\sum\limits_{n=1}^{\infty} \frac{x^n \log(n!)}{n!} \sim x \log(x) e^x$ as $x \to \infty$

asymptotics power-series approximation

Showing that $R(x)$ is a proper subset of $R((x))$ if $R$ is a field

abstract-algebra field-theory power-series

Evaluating $\sum_{n=0}^\infty\frac{(-1)^n}{3n+1}$ [closed]

calculus sequences-and-series power-series

A simple series $\sum_{i=1}^\infty \frac{i}{2^i} = 2$ [duplicate]

sequences-and-series power-series taylor-expansion

How to construct this Laurent series?

complex-analysis analysis power-series

Write $\frac {1}{1+z^2}$ as a power series centered at $z_0=1$

sequences-and-series power-series geometric-series

Compute $\sum\limits_{n=0}^{\infty}\frac{{x^n}{z^n}}{n\beta + \alpha}$

sequences-and-series power-series

Asymptotic behavior of $\sum\limits_{k=1}^n \frac{2^k}{k}$

sequences-and-series asymptotics power-series

Given a perturbation of a symmetric matrix, find an expansion for the eigenvalues

linear-algebra matrices power-series

Series expansion: $1/(1-x)^n$

power-series taylor-expansion

Calculating Arc Hyperbolic CoSecant faster than using a standard power series

sequences-and-series trigonometry power-series trigonometric-series

sequence problems and partial sums

sequences-and-series power-series

When is it invalid to use taylor series expansion?

polynomials power-series taylor-expansion

Limit of a power series in $\beta$ multiplied by $(1 - \beta)$

limits power-series limsup-and-liminf divergent-series analyticity