Question

Solution to $y''+(1-x)y'+y=0$ using power series, where $y=\sum_{n=0}^{\infty}a_{n}x^{n}$

score 3.1k · Answer 1 · 2018-02-16 19:09:32

3.1k

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Solution to $y''+(1-x)y'+y=0$ using power series, where $y=\sum_{n=0}^{\infty}a_{n}x^{n}$

Published on 16 Feb 2018 - 19:09

score 64 · Answer 2 · 2018-02-18 02:53:10

64

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Taylor series boundary behavior if the coefficients are not absolutely summable

Published on 18 Feb 2018 - 2:53

score 399 · Answer 3 · 2018-02-18 12:42:18

399

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Power series converging at $1$ with all derivatives zero

Published on 18 Feb 2018 - 12:42

score 2.4k · Answer 4 · 2026-03-22 11:19:33

2.4k

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Understanding the branch cut and discontinuity of the hypergeometric function

Published on 22 Mar 2026 - 11:19

score 187 · Answer 5 · 2018-02-19 15:11:26

187

Views

Finding the radius of convergence of a cubic Taylor series

Published on 19 Feb 2018 - 15:11

score 34 · Answer 6 · 2026-03-25 04:41:38

34

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Radius of convergence of $\sum_{n=0}^\infty \frac{z^n}{e^{an}+1}, a \in \mathbb{C}$

Published on 25 Mar 2026 - 4:41

score 2.9k · Answer 7 · 2018-02-20 15:11:15

2.9k

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For which values of $x$ does these series converge absolutely, converge conditionally or diverge

Published on 20 Feb 2018 - 15:11

score 91 · Answer 8 · 2026-03-22 18:25:00

91

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Find the value of $R$ such that $\sum_{n=0}^{\infty} \frac{x^n}{n! \cdot (\ln 3)^n} = 3^x, \forall x \in (-R,R)$

Published on 22 Mar 2026 - 18:25

score 42 · Answer 9 · 2026-03-21 18:14:46

42

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Diagonal power series

Published on 21 Mar 2026 - 18:14

score 608 · Answer 10 · 2026-03-22 03:21:12

608

Views

p-adic binomial series

Published on 22 Mar 2026 - 3:21

score 48 · Answer 11 · 2018-02-21 15:36:06

What could be a good example for: $\frac{\rm d}{{\rm d}x}\sum_{n\in\mathbb N}f_n(x)\neq \sum_{n\in\mathbb N}\frac{\rm d}{{\rm d}x}f_n(x)$?

score 390 · Answer 12 · 2026-03-20 13:06:33

390

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Find the Cauchy product of $e^x$ and $e^{-x}$.

Published on 20 Mar 2026 - 13:06

score 116 · Answer 13 · 2026-03-22 16:28:44

116

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Convergence of $\sum_{k=0}^{\infty} a^k\cdot b^{k^2}$

Published on 22 Mar 2026 - 16:28

score 806 · Answer 14 · 2018-02-23 01:28:25

806

Views

Power Series of $\ \frac x3 \ln(1+x^2).$

Published on 23 Feb 2018 - 1:28

score 489 · Answer 15 · 2018-02-23 01:48:43

489

Views

Series of $-\sum_{k=1}^{\infty}\frac{(-1)^k}{1+k^2}$

Published on 23 Feb 2018 - 1:48

List Question

Solution to $y''+(1-x)y'+y=0$ using power series, where $y=\sum_{n=0}^{\infty}a_{n}x^{n}$

Taylor series boundary behavior if the coefficients are not absolutely summable

Power series converging at $1$ with all derivatives zero

Understanding the branch cut and discontinuity of the hypergeometric function

Finding the radius of convergence of a cubic Taylor series

Radius of convergence of $\sum_{n=0}^\infty \frac{z^n}{e^{an}+1}, a \in \mathbb{C}$

For which values of $x$ does these series converge absolutely, converge conditionally or diverge

Find the value of $R$ such that $\sum_{n=0}^{\infty} \frac{x^n}{n! \cdot (\ln 3)^n} = 3^x, \forall x \in (-R,R)$

Diagonal power series

p-adic binomial series

What could be a good example for: $\frac{\rm d}{{\rm d}x}\sum_{n\in\mathbb N}f_n(x)\neq \sum_{n\in\mathbb N}\frac{\rm d}{{\rm d}x}f_n(x)$?

Find the Cauchy product of $e^x$ and $e^{-x}$.

Convergence of $\sum_{k=0}^{\infty} a^k\cdot b^{k^2}$

Power Series of $\ \frac x3 \ln(1+x^2).$

Series of $-\sum_{k=1}^{\infty}\frac{(-1)^k}{1+k^2}$

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