List questions from power-series

Published on 05 Apr 2026 - 23:46

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Uniform convergence and differentiability of $\ \sum_{n=1}^\infty \frac{1}{nx}(1-e^{-\frac{x}{n}}) $

Published on 05 Apr 2026 - 23:46

33

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Proofs of differentiability

Published on 05 Apr 2026 - 23:38

104

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Why does $\sum_{i,j}^\infty \frac{1}{i(i^2+j^2)}$ converge?

Published on 29 Apr 2020 - 22:45

33

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Continuity of a specific Power Series

Published on 30 Apr 2020 - 9:52

139

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Prove that a power series $f(x)$ satisfies $-f''(x) + x^2f(x) = 3f(x) \ \text{for all} \ x \in \mathbb{R}$.

Published on 30 Apr 2020 - 10:39

60

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Recurrence relation problem with $a_{n-1}=2a_n+4^n$ for $n\geqslant 0$, and $a_1=3$.

Published on 01 Apr 2026 - 22:26

43

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One property of a power series

Published on 11 Apr 2026 - 16:47

175

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Combining expression to form a single power series

Published on 01 May 2020 - 10:08

3.7k

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Solve $x(1-x)y''+2(1-2x)y'-2y=0$ by the Frobenius Method

Published on 09 Apr 2026 - 6:07

190

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A problem on power series from chapter 24 of Spivak Calculus 3rd Edition

Published on 12 Apr 2026 - 3:06

1.4k

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Power series method to solve $(1-x^2)y^{\prime\prime}+2xy^{\prime}-2y=0$

Published on 02 May 2020 - 11:56

212

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proving: $(1+x)(1+x^2)(1+x^3)\ldots = \frac{1}{(1-x)(1-x^3)(1-x^5)\ldots}$

Published on 28 Mar 2026 - 15:21

263

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Sum the series of $\sum\limits_{n=1}^{\infty} \frac{1}{2^n n} $

Published on 02 May 2020 - 15:09

78

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Random power series and zeros

Published on 12 Apr 2026 - 2:56

List Question

Check the uniform convergence of $\ \sum_{n=1}^\infty x^ne^{-xn} $

Uniform convergence and differentiability of $\ \sum_{n=1}^\infty \frac{1}{nx}(1-e^{-\frac{x}{n}}) $

Proofs of differentiability

Why does $\sum_{i,j}^\infty \frac{1}{i(i^2+j^2)}$ converge?

Continuity of a specific Power Series

Prove that a power series $f(x)$ satisfies $-f''(x) + x^2f(x) = 3f(x) \ \text{for all} \ x \in \mathbb{R}$.

Recurrence relation problem with $a_{n-1}=2a_n+4^n$ for $n\geqslant 0$, and $a_1=3$.

One property of a power series

Combining expression to form a single power series

Solve $x(1-x)y''+2(1-2x)y'-2y=0$ by the Frobenius Method

A problem on power series from chapter 24 of Spivak Calculus 3rd Edition

Power series method to solve $(1-x^2)y^{\prime\prime}+2xy^{\prime}-2y=0$

proving: $(1+x)(1+x^2)(1+x^3)\ldots = \frac{1}{(1-x)(1-x^3)(1-x^5)\ldots}$

Sum the series of $\sum\limits_{n=1}^{\infty} \frac{1}{2^n n} $

Random power series and zeros

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