New posts in power-series

Solving a formal power series equation

real-analysis algebra-precalculus sequences-and-series power-series

Abel limit theorem

real-analysis sequences-and-series limits convergence-divergence power-series

$f'/f\in\mathbb{Z}[[x]]$ for polynomials vs. formal power series $f$

number-theory algebraic-number-theory power-series divisibility

Closed form of $\sum \frac{x^n}{n^n}$

power-series

Can the result of termwise multiplication of power series be found in a closed form?

combinatorics power-series closed-form

Prove the following equation of complex power series.

sequences-and-series complex-analysis complex-numbers power-series

How does one show sin(x) is bounded using the power series?

real-analysis ordinary-differential-equations inequality power-series

Origin and use of an identity of formal power series: $\det(1 - \psi T) = \exp \left(-\sum_{s=1}^{\infty} \text{Tr}(\psi^{s})T^{s}/s\right)$

linear-algebra number-theory power-series determinant p-adic-number-theory

Uniform convergence of coefficients of power series

complex-analysis power-series

Generalised Binomial Theorem Intuition

power-series

How to calculate the integral of $x^x$ between $0$ and $1$ using series? [duplicate]

calculus sequences-and-series power-series

Is there an entire function with $f(\mathbb{Q}) \subset \mathbb{Q}$ and a non-finite power series representation having only rational Coeffitients

complex-analysis power-series entire-functions transcendental-functions

Proving finite sum identity

combinatorics power-series

Finding $\limsup_{n\to\infty}\sqrt[n]{|a_n|}$ for a recursively defined sequence $(a_n)$ with $a_{n}=\frac13(a_{n-1}+a_{n-2}+a_{n-1}a_{n-2})$

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

How can I continue my proof that the difference of cosine integrals is the Euler Mascheroni constant?

calculus power-series trigonometric-integrals euler-mascheroni-constant

Prove sum of $\cos(\pi/11)+\cos(3\pi/11)+...+\cos(9\pi/11)=1/2$ using Euler's formula

trigonometry power-series

power series with binomial coefficient

real-analysis power-series binomial-coefficients

Sums of $5$th and $7$th powers of natural numbers: $\sum\limits_{i=1}^n i^5+i^7=2\left( \sum\limits_{i=1}^ni\right)^4$?

sequences-and-series elementary-number-theory summation power-series perfect-powers

Show that entire function $f$ is a polynomial of degree at most $n$

complex-analysis power-series complex-integration

Could we show $1-(x-\frac{x^3}{3!}+\frac{x^5}{5!}-\dots)^2=(1-\frac{x^2}{2!}+\frac{x^4}{4!}- \dots)^2$ if we didn't know about Taylor Expansion?

sequences-and-series trigonometry power-series