Question

Why doesn't the Taylor expansion at 0 around $ e^{-1/x^2} $ converge to the function itself?

score 477 · Answer 1 · 2019-12-03 03:05:38

477

Views

Why doesn't the Taylor expansion at 0 around $ e^{-1/x^2} $ converge to the function itself?

Published on 03 Dec 2019 - 3:05

score 622 · Answer 2 · 2019-12-03 12:29:32

622

Views

Taylor expansion of $\exp(\sin x)$ around $c=0$

Published on 03 Dec 2019 - 12:29

score 105 · Answer 3 · 2026-03-27 06:07:56

105

Views

Maclaurin Series for $\operatorname{erf}(z)$

Published on 27 Mar 2026 - 6:07

score 80 · Answer 4 · 2019-12-03 19:29:09

80

Views

Prove $ 1+\left( 1-\frac{x}{n}\right)+...+\left(1-\frac{x}{n}\right)^{n-1}=\frac{n}{x}\left(1-\left(1-\frac{x}{n}\right)^n\right)$

Published on 03 Dec 2019 - 19:29

score 2k · Answer 5 · 2019-12-03 22:53:18

2k

Views

Finding the Maclaurin series for $f(x)=x\ln(x+1)$

Published on 03 Dec 2019 - 22:53

score 223 · Answer 6 · 2026-04-06 22:48:59

223

Views

Asymptotic of gaussian integral

Published on 06 Apr 2026 - 22:48

score 109 · Answer 7 · 2019-12-04 20:10:36

109

Views

Taylor expansion with Gaussian perturbation

Published on 04 Dec 2019 - 20:10

score 49 · Answer 8 · 2026-04-04 08:46:28

49

Views

Give an example of a function that converges to its Taylor series for $x\geq 0$ but not for $x<0$.

Published on 04 Apr 2026 - 8:46

score 114 · Answer 9 · 2019-12-06 12:54:00

114

Views

Find Taylor Series of $(3x^2 + 2x -7)e^{5x}$

Published on 06 Dec 2019 - 12:54

score 42 · Answer 10 · 2019-12-06 15:28:16

42

Views

Calculate $\sum^\infty _{k=1} \frac{10^{-k-1}}{k(k+1)}$ using the Taylor series of $(1-x)\ln(1-x)$

Published on 06 Dec 2019 - 15:28

score 258 · Answer 11 · 2019-12-07 04:11:32

258

Views

Substitution in the taylor series of $\ln(1+ x)$

Published on 07 Dec 2019 - 4:11

score 1.3k · Answer 12 · 2019-12-07 06:59:33

1.3k

Views

Taylor Series expansion of a function around a point but what point

Published on 07 Dec 2019 - 6:59

score 44 · Answer 13 · 2019-12-07 12:20:49

44

Views

Proving Taylor's Theorem On Two Vriables

Published on 07 Dec 2019 - 12:20

score 1.8k · Answer 14 · 2019-12-07 13:06:59

1.8k

Views

The convergence of power series of $\log(1+x)$ with or without Taylor expansion

Published on 07 Dec 2019 - 13:06

score 47 · Answer 15 · 2019-12-07 21:13:36

47

Views

Is my usage of $O$ notation correct here? Series $\sum (n^{1/n}-1)$ and $\sum \log(1+\frac{1}{n\sqrt{n}})$

Published on 07 Dec 2019 - 21:13

List Question

Why doesn't the Taylor expansion at 0 around $ e^{-1/x^2} $ converge to the function itself?

Taylor expansion of $\exp(\sin x)$ around $c=0$

Maclaurin Series for $\operatorname{erf}(z)$

Prove $ 1+\left( 1-\frac{x}{n}\right)+...+\left(1-\frac{x}{n}\right)^{n-1}=\frac{n}{x}\left(1-\left(1-\frac{x}{n}\right)^n\right)$

Finding the Maclaurin series for $f(x)=x\ln(x+1)$

Asymptotic of gaussian integral

Taylor expansion with Gaussian perturbation

Give an example of a function that converges to its Taylor series for $x\geq 0$ but not for $x<0$.

Find Taylor Series of $(3x^2 + 2x -7)e^{5x}$

Calculate $\sum^\infty _{k=1} \frac{10^{-k-1}}{k(k+1)}$ using the Taylor series of $(1-x)\ln(1-x)$

Substitution in the taylor series of $\ln(1+ x)$

Taylor Series expansion of a function around a point but what point

Proving Taylor's Theorem On Two Vriables

The convergence of power series of $\log(1+x)$ with or without Taylor expansion

Is my usage of $O$ notation correct here? Series $\sum (n^{1/n}-1)$ and $\sum \log(1+\frac{1}{n\sqrt{n}})$

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