Question

Find function whose power series is $\sum\frac{(-1)^n}{(2n)!}x^n$

score 1.1k · Answer 1 · 2019-01-01 21:53:36

1.1k

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Find function whose power series is $\sum\frac{(-1)^n}{(2n)!}x^n$

Published on 01 Jan 2019 - 21:53

score 241 · Answer 2 · 2026-03-26 12:58:04

241

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Shw that $ \ (1+X)^a \in \mathbb{Q}$ both in $\mathbb{R}$ and $ \mathbb{Q}_p$ under some condition

Published on 26 Mar 2026 - 12:58

score 351 · Answer 3 · 2019-01-02 13:04:55

351

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How to calculate a series with complex numbers?

Published on 02 Jan 2019 - 13:04

score 1.8k · Answer 4 · 2026-03-25 15:43:46

1.8k

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Why is $\cos \sqrt z$ entire but $\sin \sqrt{z}$ isn't?

Published on 25 Mar 2026 - 15:43

score 48 · Answer 5 · 2019-01-03 14:35:45

48

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How to get the coefficients of a power series without multiplying

Published on 03 Jan 2019 - 14:35

score 1.1k · Answer 6 · 2019-01-03 16:25:38

1.1k

Views

How to take every third element in a series?

Published on 03 Jan 2019 - 16:25

score 27 · Answer 7 · 2026-03-25 15:42:31

27

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absolut and uniform convergence of complex power series on an open disk imply absolut and local uniform convergence on the whole disk of convergence

Published on 25 Mar 2026 - 15:42

score 327 · Answer 8 · 2019-01-04 19:54:40

327

Views

power series expansion in two variables

Published on 04 Jan 2019 - 19:54

score 50 · Answer 9 · 2019-01-04 23:30:24

50

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Questions about the powerseries $\sum_{n=0}^{\infty}\frac{1}{n^d}z^n,d\in\mathbb{R},z\in\mathbb{C}$

Published on 04 Jan 2019 - 23:30

score 30 · Answer 10 · 2019-01-05 00:28:49

30

Views

What is the convergence behaviour for $\sum_{n=0}^{\infty}\frac{1}{n^d}z^n$ with $z\in\mathbb{C},|z|=1$ and $0 < d \leq 1$?

Published on 05 Jan 2019 - 0:28

score 797 · Answer 11 · 2026-03-26 09:50:06

797

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Do the zeroes of this polynomial lie inside, outside, or on the unit circle? $P_n(z)=1^3 z + 2^3 z^2 + 3^3 z^3 + \cdots + n^3 z^n$

Published on 26 Mar 2026 - 9:50

score 181 · Answer 12 · 2026-03-26 18:58:43

181

Views

A function holomorphic on $\mathbb{D}(0,2)$ and bounded on a unit circle is a polynomial

Published on 26 Mar 2026 - 18:58

score 91 · Answer 13 · 2019-01-05 20:29:48

91

Views

Analytic or perturbative solution in any limits?

Published on 05 Jan 2019 - 20:29

score 257 · Answer 14 · 2019-01-06 10:41:40

257

Views

Fubini's theorem for series with dependent indices

Published on 06 Jan 2019 - 10:41

score 64 · Answer 15 · 2019-01-06 13:23:37

64

Views

Why radius of convergence of a power series can only be real

Published on 06 Jan 2019 - 13:23

List Question

Find function whose power series is $\sum\frac{(-1)^n}{(2n)!}x^n$

Shw that $ \ (1+X)^a \in \mathbb{Q}$ both in $\mathbb{R}$ and $ \mathbb{Q}_p$ under some condition

How to calculate a series with complex numbers?

Why is $\cos \sqrt z$ entire but $\sin \sqrt{z}$ isn't?

How to get the coefficients of a power series without multiplying

How to take every third element in a series?

absolut and uniform convergence of complex power series on an open disk imply absolut and local uniform convergence on the whole disk of convergence

power series expansion in two variables

Questions about the powerseries $\sum_{n=0}^{\infty}\frac{1}{n^d}z^n,d\in\mathbb{R},z\in\mathbb{C}$

What is the convergence behaviour for $\sum_{n=0}^{\infty}\frac{1}{n^d}z^n$ with $z\in\mathbb{C},|z|=1$ and $0 < d \leq 1$?

Do the zeroes of this polynomial lie inside, outside, or on the unit circle? $P_n(z)=1^3 z + 2^3 z^2 + 3^3 z^3 + \cdots + n^3 z^n$

A function holomorphic on $\mathbb{D}(0,2)$ and bounded on a unit circle is a polynomial

Analytic or perturbative solution in any limits?

Fubini's theorem for series with dependent indices

Why radius of convergence of a power series can only be real

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