New posts in power-series

${a_n}$ series of Fibonacci numbers. $f(x)=\sum_{0}^{\infty}a_nx^n$, show that in the convergence radius: $f(x)= \frac{1}{1-x-x^2}$

calculus convergence-divergence power-series

A conjecture formula: $\sum\limits_{n=1}^\infty \frac{\binom{mn}{n}}{n}\left(\frac{(m-1)^{m-1}}{m^m} \right)^n=m\log\left(\frac{m}{m-1}\right)$

power-series binomial-coefficients

Finding the $18th$ Derivative of a Particular Product at $x = 0$

derivatives solution-verification power-series diophantine-equations

Power series that diverges in specified number of points on the circle of convergence

complex-analysis power-series

What is $\lim_{x\to1^{-}} (1-x)\left(\sum_{i=0}^{\infty} x^{i^2}\right)^{2}$?

calculus sequences-and-series limits power-series

Finding the power series for $y$ where $y + \sin(y) = x$

sequences-and-series power-series

Can there be more than one power series expansion for a function.

calculus integration sequences-and-series algebra-precalculus power-series

Prove that $\exp(\log(\frac{1}{1-x})) = \frac{1}{1-x}$

combinatorics binomial-coefficients power-series generating-functions

How to solve $y''-y=\sin(x)$ using power series?

ordinary-differential-equations power-series

Is this generalization of an exercise in Stein true?

complex-analysis power-series

Taylor series for different points... how do they look?

analysis power-series taylor-expansion

How to create alternating series with happening every two terms

calculus sequences-and-series power-series

What is the corresponding infinite series for this infinite infinite product?

real-analysis sequences-and-series functions power-series infinite-product

How did Ramanujan find this formula?

sequences-and-series number-theory power-series math-history

Lagrange Bürmann Inversion Series Example

real-analysis complex-analysis power-series taylor-expansion implicit-function-theorem

Can $\sum_{n=0}^\infty a_nx_i^n = \sum_{n=0}^\infty b_nx_i^n$ for distinct $(x_i)_{i\in \mathbb{N}}$ from interval $(0,1)$?

analysis power-series analytic-functions

closed form for a series over the Riemann zeta zeros

number-theory power-series riemann-zeta

How can we show that $ \sum_{n=0}^{\infty}\frac{2^nn[n(\pi^3+1)+\pi^2](n^2+n-1)}{(2n+1)(2n+3){2n \choose n}}=1+\pi+\pi^2+\pi^3+\pi^4 ?$

sequences-and-series summation power-series

If $\lim_{x\to\infty} [f(x+1)-f(x)] =l$ then $\lim_{ x\to\infty}f(x)/x =l$ ($f$ is continuous)

calculus functional-analysis limits power-series

How to prove this series about Fibonacci number: $\sum_{n=1}^{\infty }\frac{F_{n}}{2^{n}}=2$? [duplicate]

calculus sequences-and-series power-series closed-form fibonacci-numbers