New posts in power-series

Equality with Euler–Mascheroni constant

calculus power-series euler-mascheroni-constant

The value of a limit of a power series: $\lim\limits_{x\rightarrow +\infty} \sum_{k=1}^\infty (-1)^k \left(\frac{x}{k} \right)^k$

sequences-and-series limits power-series

A "relative" of the exponential function

power-series exponential-function special-functions volume

Finding the sum of the infinite series whose general term is not easy to visualize: $\frac16+\frac5{6\cdot12}+\frac{5\cdot8}{6\cdot12\cdot18}+\cdots$ [duplicate]

real-analysis sequences-and-series power-series

$(1+x)^a$ McLaurin series

real-analysis calculus power-series

counterexample to Abel's theorem

sequences-and-series complex-analysis power-series

Prove that the radius of derived series $\sigma'$ is the same of $\sigma$.

real-analysis sequences-and-series solution-verification proof-explanation power-series

How to analyze $\sup_{x>0}|e^xf(x)| < \infty$ and $\sup_{n\in\mathbb{N}} |f^{(n)}(0)|< \infty$?

real-analysis complex-analysis power-series

composition of power series

real-analysis complex-analysis power-series analyticity

Power series of $x/(1-ae^{-x})$.

power-series bernoulli-numbers eulerian-numbers

Expressing the area of the image of a holomorphic function by the coefficients of its expansion

complex-analysis integration power-series analyticity

Write out the following equation as a power series

calculus combinatorics discrete-mathematics power-series

Puiseux series over an algebraically closed field

abstract-algebra field-theory power-series

Show that $\lim _{x\rightarrow 1}\frac{\sum _{n=0}^{\infty }a_nx^{n\ }}{\frac{1}{1-x}\log \left(\frac{1}{1-x}\right)} = 1$

real-analysis calculus sequences-and-series power-series

How to do a very long division: continued fraction for tan

number-theory trigonometry power-series continued-fractions

Power series which diverges precisely at the roots of unity, converges elsewhere

complex-analysis convergence-divergence power-series conditional-convergence

How do you prove the Cauchy product (multiplication) of two infinite power series (generating functions) which have different exponents/indices?

combinatorics complex-analysis power-series generating-functions cauchy-product

Did Feynman mentally compute $\sqrt[3]{1729.03}$ by linear approximation?

calculus numerical-methods power-series popular-math mental-arithmetic

Radius of convergence of $\sum_{n=0}^\infty n!x^{n^2}$

power-series

Solving the recursion $3a_{n+1}=2(n+1)a_n+5(n+1)!$ via generating functions

recurrence-relations power-series generating-functions