Question

Show existence of power series that meets the condition of the differential equation $y''-xy=0, y(0) = 1, y'(0) = 0$

score 108 · Answer 1 · 2019-11-20 16:36:09

108

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Show existence of power series that meets the condition of the differential equation $y''-xy=0, y(0) = 1, y'(0) = 0$

Published on 20 Nov 2019 - 16:36

score 170 · Answer 2 · 2019-11-21 02:33:44

170

Views

Series expansion for irrational functions such as $\dfrac{1}{\sqrt{1+x+x^2}}$

Published on 21 Nov 2019 - 2:33

score 55 · Answer 3 · 2019-11-21 03:02:58

55

Views

Power series $f(x)=\frac1{(1+x)^2}$

Published on 21 Nov 2019 - 3:02

score 68 · Answer 4 · 2026-03-25 06:58:56

68

Views

What is the limit of the nth root of a sequenc which diverges?

Published on 25 Mar 2026 - 6:58

score 105 · Answer 5 · 2026-03-30 04:59:07

105

Views

Periodicity of a Certain Generalized Power Series

Published on 30 Mar 2026 - 4:59

score 173 · Answer 6 · 2019-11-22 20:34:12

173

Views

Find the closed form generating function for the following series

Published on 22 Nov 2019 - 20:34

score 1.1k · Answer 7 · 2026-04-07 01:03:57

1.1k

Views

Bernoulli numbers and $\tan(x)$ expansion

Published on 07 Apr 2026 - 1:03

score 127 · Answer 8 · 2026-04-07 22:33:29

127

Views

Is it possible to express a function in terms of a power series of any arbitrary function?

Published on 07 Apr 2026 - 22:33

score 139 · Answer 9 · 2019-11-23 20:03:01

139

Views

Why we can write functions as "infinite" power series?

Published on 23 Nov 2019 - 20:03

score 898 · Answer 10 · 2026-04-07 02:32:07

898

Views

What is wrong with my series expansion of $e^{\cos(x)}$

Published on 07 Apr 2026 - 2:32

score 105 · Answer 11 · 2026-03-26 03:06:11

105

Views

Find the closed form for the following power series

Published on 26 Mar 2026 - 3:06

score 137 · Answer 12 · 2026-04-07 02:36:11

137

Views

Show that there is an infinitely differentiable function f(x), such that the radius of convergence of its Taylor series equals to 0

Published on 07 Apr 2026 - 2:36

score 849 · Answer 13 · 2019-11-26 20:57:26

849

Views

What is wrong with my series expansion of $\cos(\sin(x))$

Published on 26 Nov 2019 - 20:57

score 603 · Answer 14 · 2019-11-26 20:59:22

$\sum_{n=0}^\infty C_n(x-3)^n$ converges for $x=0$, and diverges for $x=7$. Does $\sum C_n$ converge? $\sum C_n5^n$? $\sum C_n\frac{2^{n+1}}{n+1}$?

score 54 · Answer 15 · 2019-11-26 23:21:12

54

Views

Equality of $2$ infinite series

Published on 26 Nov 2019 - 23:21

List Question

Show existence of power series that meets the condition of the differential equation $y''-xy=0, y(0) = 1, y'(0) = 0$

Series expansion for irrational functions such as $\dfrac{1}{\sqrt{1+x+x^2}}$

Power series $f(x)=\frac1{(1+x)^2}$

What is the limit of the nth root of a sequenc which diverges?

Periodicity of a Certain Generalized Power Series

Find the closed form generating function for the following series

Bernoulli numbers and $\tan(x)$ expansion

Is it possible to express a function in terms of a power series of any arbitrary function?

Why we can write functions as "infinite" power series?

What is wrong with my series expansion of $e^{\cos(x)}$

Find the closed form for the following power series

Show that there is an infinitely differentiable function f(x), such that the radius of convergence of its Taylor series equals to 0

What is wrong with my series expansion of $\cos(\sin(x))$

$\sum_{n=0}^\infty C_n(x-3)^n$ converges for $x=0$, and diverges for $x=7$. Does $\sum C_n$ converge? $\sum C_n5^n$? $\sum C_n\frac{2^{n+1}}{n+1}$?

Equality of $2$ infinite series

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