Question

Deterministic radius of convergence of power series

score 361 · Answer 1 · 2019-12-10 19:45:25

361

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Deterministic radius of convergence of power series

Published on 10 Dec 2019 - 19:45

score 662 · Answer 2 · 2026-03-28 00:49:16

662

Views

Using $\limsup |a_n|^{1/n}$ to find radius of convergence of a power series.

Published on 28 Mar 2026 - 0:49

score 214 · Answer 3 · 2019-12-11 04:20:06

214

Views

Computation question regarding a power series solution to differential equation.

Published on 11 Dec 2019 - 4:20

score 172 · Answer 4 · 2026-03-27 11:49:00

172

Views

Fibonacci sum for $\pi$: $\sum_{n=1}^\infty\frac{F_{2n}}{n^2\binom{2n}{n}}=\frac{4\pi^2}{25\sqrt5}$

Published on 27 Mar 2026 - 11:49

score 97 · Answer 5 · 2019-12-11 11:54:02

97

Views

Power series by algebraic numbers

Published on 11 Dec 2019 - 11:54

score 118 · Answer 6 · 2026-03-27 12:02:51

118

Views

Repetitive 1-9 pow last digit

Published on 27 Mar 2026 - 12:02

score 49 · Answer 7 · 2019-12-12 00:46:07

49

Views

Proof $\sum_{k=0}^\infty a_k(z-z_0)^k$ diverges for $|z-z_0| > 1/a$, converges for $|z-z_0| < 1/a$ and absolutely converges for $a=0$?

Published on 12 Dec 2019 - 0:46

score 160 · Answer 8 · 2019-12-12 01:05:40

160

Views

Convergence radius of $\sum_{k=0}^\infty \frac{\binom{2k}{k}}{k^k}z^k$

Published on 12 Dec 2019 - 1:05

score 37 · Answer 9 · 2019-12-12 12:03:08

37

Views

$1+z(z+1)(1+z)^2$ and $\frac{1}{1+z^2}$ as power series

Published on 12 Dec 2019 - 12:03

score 32 · Answer 10 · 2026-04-07 09:24:36

32

Views

Can a function differ from its Taylor series but converge like its Taylor series?

Published on 07 Apr 2026 - 9:24

score 330 · Answer 11 · 2026-04-07 09:25:34

330

Views

Find an integral splitting it into the power series

Published on 07 Apr 2026 - 9:25

score 64 · Answer 12 · 2026-03-26 03:02:32

64

Views

Represent $f(x)$ with $g(x)$ when the taylor expension has specific dependency

Published on 26 Mar 2026 - 3:02

score 45 · Answer 13 · 2019-12-15 11:01:22

45

Views

Show that $\frac{1}{e^{t}-1} = \sum_{n=1}^{\infty} e^{-n t} $

Published on 15 Dec 2019 - 11:01

score 263 · Answer 14 · 2026-03-25 21:01:22

263

Views

$x\mapsto \frac{1}{1+x^2}$ is analytic

Published on 25 Mar 2026 - 21:01

score 225 · Answer 15 · 2026-04-07 02:09:24

225

Views

$\cosh(z) := \sum_{k=0}^\infty \frac{z^{2k}}{(2k)!}, z \in \mathbb{C}$ and $\cosh(z) = \frac{1}{2} (\exp(z)+\exp(-z))$

Published on 07 Apr 2026 - 2:09

List Question

Deterministic radius of convergence of power series

Using $\limsup |a_n|^{1/n}$ to find radius of convergence of a power series.

Computation question regarding a power series solution to differential equation.

Fibonacci sum for $\pi$: $\sum_{n=1}^\infty\frac{F_{2n}}{n^2\binom{2n}{n}}=\frac{4\pi^2}{25\sqrt5}$

Power series by algebraic numbers

Repetitive 1-9 pow last digit

Proof $\sum_{k=0}^\infty a_k(z-z_0)^k$ diverges for $|z-z_0| > 1/a$, converges for $|z-z_0| < 1/a$ and absolutely converges for $a=0$?

Convergence radius of $\sum_{k=0}^\infty \frac{\binom{2k}{k}}{k^k}z^k$

$1+z(z+1)(1+z)^2$ and $\frac{1}{1+z^2}$ as power series

Can a function differ from its Taylor series but converge like its Taylor series?

Find an integral splitting it into the power series

Represent $f(x)$ with $g(x)$ when the taylor expension has specific dependency

Show that $\frac{1}{e^{t}-1} = \sum_{n=1}^{\infty} e^{-n t} $

$x\mapsto \frac{1}{1+x^2}$ is analytic

$\cosh(z) := \sum_{k=0}^\infty \frac{z^{2k}}{(2k)!}, z \in \mathbb{C}$ and $\cosh(z) = \frac{1}{2} (\exp(z)+\exp(-z))$

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