Question

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

score 146 · Answer 1 · 2019-02-06 14:34:29

146

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

Published on 06 Feb 2019 - 14:34

score 73 · Answer 2 · 2019-02-07 00:59:58

73

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Calculating $\sum_{n=0}^\infty\frac{(n+1)(n+2)}{2}x^n$ when $|x|<1$

Published on 07 Feb 2019 - 0:59

score 500 · Answer 3 · 2019-02-07 08:14:25

500

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Radius of convergence of series $\sum a_n x^{n^2}$ such that $a_0=1$ and $a_n=3^{-n}a_{n-1}$ for all $n\in\mathbb N$

Published on 07 Feb 2019 - 8:14

score 200 · Answer 4 · 2026-03-25 12:53:05

200

Views

On the Newton Polygon for $p-$adic Power series

Published on 25 Mar 2026 - 12:53

score 45 · Answer 5 · 2026-03-27 07:31:12

45

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Proving formal power series $A(x) = \sum_{n = 0}^{\infty} a_nx^n$ with $A'(x) := \sum_{n=0}^{\infty}(n+1)a_{n+1}x^n$

Published on 27 Mar 2026 - 7:31

score 88 · Answer 6 · 2019-02-08 11:20:39

88

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Radius of convergence of $\sum_{n\ge 1}\frac{z^n}{n}$

Published on 08 Feb 2019 - 11:20

score 40 · Answer 7 · 2026-03-29 21:54:04

40

Views

Uniform convergence of $f_n (x)=x^{2} - \frac{x}{n}$ on $[0, 1]$.

Published on 29 Mar 2026 - 21:54

score 173 · Answer 8 · 2026-03-26 22:29:40

173

Views

How to find the second solution to an ODE of the form $xy''+y'-xy=0$?

Published on 26 Mar 2026 - 22:29

score 293 · Answer 9 · 2026-03-27 17:35:22

293

Views

What is the series expansion of $ \sqrt[x] x $?

Published on 27 Mar 2026 - 17:35

score 5.3k · Answer 10 · 2019-02-10 07:33:06

5.3k

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Power series solution to $y’ + 2xy = 0$

Published on 10 Feb 2019 - 7:33

score 244 · Answer 11 · 2026-03-27 17:37:17

244

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How would we find $ \int \sqrt[x]{x}$ or $\int \left( x^{x^{x^{.^{....... \infty}}}} \right) dx$?

Published on 27 Mar 2026 - 17:37

score 1.5k · Answer 12 · 2019-02-10 16:24:08

1.5k

Views

Series Solution to the ODE $y''+2y'+y=0$

Published on 10 Feb 2019 - 16:24

score 347 · Answer 13 · 2026-03-27 17:35:20

347

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How to find $\int \sum_{n=0}^\infty \frac {(\ln x)^n}{x^n.n!}dx $?

Published on 27 Mar 2026 - 17:35

score 42 · Answer 14 · 2019-02-11 01:57:03

42

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Show that $ \int_0^xe^{x-t}f(t)dt=\sum_{n=0}^\infty( f^{(n)}(0)(e^x-\sum_{i=0}^n \frac{x^i}{i!}))$ ,$-R\lt x\lt R$.

Published on 11 Feb 2019 - 1:57

score 67 · Answer 15 · 2026-03-29 21:54:06

67

Views

Uniform convergence of series of functions given convergence of coefficients

Published on 29 Mar 2026 - 21:54

List Question

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

Calculating $\sum_{n=0}^\infty\frac{(n+1)(n+2)}{2}x^n$ when $|x|<1$

Radius of convergence of series $\sum a_n x^{n^2}$ such that $a_0=1$ and $a_n=3^{-n}a_{n-1}$ for all $n\in\mathbb N$

On the Newton Polygon for $p-$adic Power series

Proving formal power series $A(x) = \sum_{n = 0}^{\infty} a_nx^n$ with $A'(x) := \sum_{n=0}^{\infty}(n+1)a_{n+1}x^n$

Radius of convergence of $\sum_{n\ge 1}\frac{z^n}{n}$

Uniform convergence of $f_n (x)=x^{2} - \frac{x}{n}$ on $[0, 1]$.

How to find the second solution to an ODE of the form $xy''+y'-xy=0$?

What is the series expansion of $ \sqrt[x] x $?

Power series solution to $y’ + 2xy = 0$

How would we find $ \int \sqrt[x]{x}$ or $\int \left( x^{x^{x^{.^{....... \infty}}}} \right) dx$?

Series Solution to the ODE $y''+2y'+y=0$

How to find $\int \sum_{n=0}^\infty \frac {(\ln x)^n}{x^n.n!}dx $?

Show that $ \int_0^xe^{x-t}f(t)dt=\sum_{n=0}^\infty( f^{(n)}(0)(e^x-\sum_{i=0}^n \frac{x^i}{i!}))$ ,$-R\lt x\lt R$.

Uniform convergence of series of functions given convergence of coefficients

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