List questions from power-series

Published on 11 Feb 2019 - 15:35

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Show that $e^{-1/x^2}$ is not analytic around $x=0$.

Published on 25 Mar 2026 - 3:22

50

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Multinomials for negative integer powers.

Published on 25 Mar 2026 - 11:08

51

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Find $f^{(k)}(0)$ of $f(x)=\frac{\sin x}{x}$ for $x\neq 0$ and $f(0)=1$.

Published on 12 Feb 2019 - 4:20

651

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Convergence of Power Series and Power Series Solutions of ODE

Published on 25 Mar 2026 - 23:39

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Proving "$\forall_{\epsilon>0} \exists_{N \in \mathbb{N}} \forall_{n \geq N}: x^{n} < \epsilon$" for $0<x<1$.

Published on 12 Feb 2019 - 7:42

68

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Property of alternating sign series

Published on 12 Feb 2019 - 22:12

352

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If $f(x)=\sum\limits_{n=0}^\infty a_n x^n$ is even and continous, then $a_n=0$ for odd n, and if f is an odd function, then $a_n=0$ for even n.

Published on 13 Feb 2019 - 5:11

83

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Find rational representation of a power series

Published on 25 Mar 2026 - 21:23

661

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Ramanujan's Master Theorem relation to Analytic Continuation

Published on 13 Feb 2019 - 19:03

63

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Cohen Structure Theorem Hensel's Lemma

Published on 13 Feb 2019 - 20:23

95

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Is the sum of series $\sum_{n=0}^{\infty} \lfloor n\pi \rfloor x^n$ a rational function?

Published on 25 Mar 2026 - 21:22

173

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How to "directly" obtain Maclaurin series of $\exp(x-1+\sqrt{x^2+1})$

Published on 14 Feb 2019 - 3:58

57

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Contradiction in radii of convergence? Where is my error?

Published on 28 Mar 2026 - 4:42

28

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How to express a series expansion into a power law form?

Published on 16 Feb 2019 - 14:16

List Question

Radius of convergence of $f(x)=\arcsin(x)$.

Show that $e^{-1/x^2}$ is not analytic around $x=0$.

Multinomials for negative integer powers.

Find $f^{(k)}(0)$ of $f(x)=\frac{\sin x}{x}$ for $x\neq 0$ and $f(0)=1$.

Convergence of Power Series and Power Series Solutions of ODE

Proving "$\forall_{\epsilon>0} \exists_{N \in \mathbb{N}} \forall_{n \geq N}: x^{n} < \epsilon$" for $0<x<1$.

Property of alternating sign series

If $f(x)=\sum\limits_{n=0}^\infty a_n x^n$ is even and continous, then $a_n=0$ for odd n, and if f is an odd function, then $a_n=0$ for even n.

Find rational representation of a power series

Ramanujan's Master Theorem relation to Analytic Continuation

Cohen Structure Theorem Hensel's Lemma

Is the sum of series $\sum_{n=0}^{\infty} \lfloor n\pi \rfloor x^n$ a rational function?

How to "directly" obtain Maclaurin series of $\exp(x-1+\sqrt{x^2+1})$

Contradiction in radii of convergence? Where is my error?

How to express a series expansion into a power law form?

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