Question

For which value of $ \ x \in \mathbb{R} \ $ the series $ \ \sum_{n=1}^{\infty} (-1)^n \frac{1}{x^2-n^2} \ $ converges?

score 78 · Answer 1 · 2018-05-20 12:08:21

For which value of $ \ x \in \mathbb{R} \ $ the series $ \ \sum_{n=1}^{\infty} (-1)^n \frac{1}{x^2-n^2} \ $ converges?

score 2.1k · Answer 2 · 2018-05-21 21:18:34

2.1k

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Solving Recurrence Relation for Series Solution of an ODE

Published on 21 May 2018 - 21:18

score 81 · Answer 3 · 2026-03-25 02:59:26

81

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Power series of analytic function

Published on 25 Mar 2026 - 2:59

score 29 · Answer 4 · 2018-05-23 16:53:42

29

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Is the solution to this complex power series correct?

Published on 23 May 2018 - 16:53

score 33 · Answer 5 · 2018-05-23 17:03:59

33

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Is the solution to this power series correct?

Published on 23 May 2018 - 17:03

score 56 · Answer 6 · 2018-05-23 22:40:09

56

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How to solve the differential equation for power series $(1+x^2)y'' - 6xy=0$ for $x_{0}=0$

Published on 23 May 2018 - 22:40

score 633 · Answer 7 · 2018-05-24 06:21:24

633

Views

Radius of Convergence of $\sum\frac{(n!)^3}{(3n)!}z^{3n}$

Published on 24 May 2018 - 6:21

score 176 · Answer 8 · 2018-05-24 17:13:20

176

Views

What is the coefficient of $x^n$ in the expansion of $(1+x+x^2+x^3+\dots)^4$?

Published on 24 May 2018 - 17:13

score 113 · Answer 9 · 2026-03-25 06:13:12

113

Views

Series Expansion of $\int_{\mathbb{R}} \tanh\left(\beta x\right) x \exp\left(-\frac{x^2}{2}\right) \mathrm{d} x$

Published on 25 Mar 2026 - 6:13

score 44 · Answer 10 · 2018-05-26 22:13:40

44

Views

The radius of convergence of this function

Published on 26 May 2018 - 22:13

score 1.9k · Answer 11 · 2018-05-27 04:55:16

1.9k

Views

Solving first order differential equation with power series

Published on 27 May 2018 - 4:55

score 88 · Answer 12 · 2018-05-27 15:58:29

88

Views

closed formula for Sum of this series

Published on 27 May 2018 - 15:58

score 546 · Answer 13 · 2018-05-28 02:33:19

546

Views

If a power series does not converges at a point on its radius, then it cannot be analytically continued at that point.

Published on 28 May 2018 - 2:33

score 50 · Answer 14 · 2018-05-28 09:54:11

50

Views

Example of complex power series boundedly divergent on some set.

Published on 28 May 2018 - 9:54

score 58 · Answer 15 · 2018-05-30 08:07:11

58

Views

Show that the convergence radius of $\sum\limits_{n=1}^{\infty}a_nx^n$ equals $1$.

Published on 30 May 2018 - 8:07

List Question

For which value of $ \ x \in \mathbb{R} \ $ the series $ \ \sum_{n=1}^{\infty} (-1)^n \frac{1}{x^2-n^2} \ $ converges?

Solving Recurrence Relation for Series Solution of an ODE

Power series of analytic function

Is the solution to this complex power series correct?

Is the solution to this power series correct?

How to solve the differential equation for power series $(1+x^2)y'' - 6xy=0$ for $x_{0}=0$

Radius of Convergence of $\sum\frac{(n!)^3}{(3n)!}z^{3n}$

What is the coefficient of $x^n$ in the expansion of $(1+x+x^2+x^3+\dots)^4$?

Series Expansion of $\int_{\mathbb{R}} \tanh\left(\beta x\right) x \exp\left(-\frac{x^2}{2}\right) \mathrm{d} x$

The radius of convergence of this function

Solving first order differential equation with power series

closed formula for Sum of this series

If a power series does not converges at a point on its radius, then it cannot be analytically continued at that point.

Example of complex power series boundedly divergent on some set.

Show that the convergence radius of $\sum\limits_{n=1}^{\infty}a_nx^n$ equals $1$.

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