Question

Learning the process of the developing of the real function into the power series

score 153 · Answer 1 · 2019-03-19 09:05:23

153

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Learning the process of the developing of the real function into the power series

Published on 19 Mar 2019 - 9:05

score 114 · Answer 2 · 2019-03-19 16:20:53

114

Views

Find all $A$ such that $f(x) = \sum_{n \in A} \frac{x^n}{n!}$ is bounded for $x<0$

Published on 19 Mar 2019 - 16:20

score 64 · Answer 3 · 2026-03-28 10:03:51

64

Views

Coefficient of two power series

Published on 28 Mar 2026 - 10:03

score 177 · Answer 4 · 2026-03-28 11:52:10

177

Views

Find the power series representation of $\frac{1+x}{1-2x-x^2}$

Published on 28 Mar 2026 - 11:52

score 36 · Answer 5 · 2019-03-20 21:11:27

36

Views

Is the following power series expression valid?

Published on 20 Mar 2019 - 21:11

score 95 · Answer 6 · 2026-03-25 07:44:53

95

Views

On the functions $\mathrm{Gi}_{s}^{p,q}(x)=\sum\limits_{n\geq0}\frac{x^{pn+q}}{(pn+q)^s}$

Published on 25 Mar 2026 - 7:44

score 43 · Answer 7 · 2026-03-25 01:40:03

43

Views

For $y''-2\alpha y'+\frac{2}{x} y=0$ , provided that $y(x)=\sum_{n=0}^{\infty} a_nx^n$ show you can determine $a_{n+1}$ from $a_n$

Published on 25 Mar 2026 - 1:40

score 113 · Answer 8 · 2026-03-28 21:51:34

113

Views

Compute $\sum_{n\geq1}\frac{1}{\pi^2+n^2}$ by expanding $e^{\pi x}$ in its Fourier series

Published on 28 Mar 2026 - 21:51

score 104 · Answer 9 · 2026-03-27 07:35:37

104

Views

How to invert this type of infinite series?

Published on 27 Mar 2026 - 7:35

score 98 · Answer 10 · 2026-03-25 01:26:14

98

Views

Series expansion of an expression that has productlog function about -1/e

Published on 25 Mar 2026 - 1:26

score 517 · Answer 11 · 2026-03-27 10:09:39

517

Views

Solve the following differential equation: $xy''-y'+k^2y=0$

Published on 27 Mar 2026 - 10:09

score 142 · Answer 12 · 2026-03-25 17:19:22

142

Views

Proof for radius of convergence

Published on 25 Mar 2026 - 17:19

score 106 · Answer 13 · 2019-03-24 23:13:27

106

Views

If $\sum_{n=3}^{\infty}a_n x^{n}$ has radius of convergence equal $R$, how to find radius of convergence for $\sum_{n=3}^{\infty}a_n x^{n^2}$?

Published on 24 Mar 2019 - 23:13

score 52 · Answer 14 · 2019-03-25 12:19:27

52

Views

How to justify the convergence of series $\left(\frac{1}{2}\right)^{2(2k-1)}$?

Published on 25 Mar 2019 - 12:19

score 132 · Answer 15 · 2026-02-22 23:28:32

132

Views

Recurrence relation for the asymptotic expansion of an ODE

Published on 22 Feb 2026 - 23:28

List Question

Learning the process of the developing of the real function into the power series

Find all $A$ such that $f(x) = \sum_{n \in A} \frac{x^n}{n!}$ is bounded for $x<0$

Coefficient of two power series

Find the power series representation of $\frac{1+x}{1-2x-x^2}$

Is the following power series expression valid?

On the functions $\mathrm{Gi}_{s}^{p,q}(x)=\sum\limits_{n\geq0}\frac{x^{pn+q}}{(pn+q)^s}$

For $y''-2\alpha y'+\frac{2}{x} y=0$ , provided that $y(x)=\sum_{n=0}^{\infty} a_nx^n$ show you can determine $a_{n+1}$ from $a_n$

Compute $\sum_{n\geq1}\frac{1}{\pi^2+n^2}$ by expanding $e^{\pi x}$ in its Fourier series

How to invert this type of infinite series?

Series expansion of an expression that has productlog function about -1/e

Solve the following differential equation: $xy''-y'+k^2y=0$

Proof for radius of convergence

If $\sum_{n=3}^{\infty}a_n x^{n}$ has radius of convergence equal $R$, how to find radius of convergence for $\sum_{n=3}^{\infty}a_n x^{n^2}$?

How to justify the convergence of series $\left(\frac{1}{2}\right)^{2(2k-1)}$?

Recurrence relation for the asymptotic expansion of an ODE

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