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Question about the computation of a formal power series

score 135 · Answer 1 · 2020-09-27 20:32:23

135

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Question about the computation of a formal power series

Published on 27 Sep 2020 - 20:32

score 727 · Answer 2 · 2020-10-01 09:10:29

727

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Taylor series expansion of $(1+x)^\frac{1}{n}$

Published on 01 Oct 2020 - 9:10

score 111 · Answer 3 · 2020-10-02 21:39:33

111

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Expanding function into formal infinite product

Published on 02 Oct 2020 - 21:39

score 135 · Answer 4 · 2020-10-07 00:29:34

135

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Interchanging $x$ and $y$ in Taylor's Theorem for $f(x+y)$; is there a deeper reason for equality?

Published on 07 Oct 2020 - 0:29

score 36 · Answer 5 · 2020-10-10 20:13:14

36

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How could one port elementary functions to fields of characteristic $p$? Is the concept of a power series similar?

Published on 10 Oct 2020 - 20:13

score 91 · Answer 6 · 2020-10-20 01:08:51

91

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Deriving a power series

Published on 20 Oct 2020 - 1:08

score 56 · Answer 7 · 2020-10-21 09:18:43

56

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How to interpret this q-binomial limit

Published on 21 Oct 2020 - 9:18

score 148 · Answer 8 · 2020-10-21 13:45:06

148

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Let $f(n)=\sum_{k=0}^{\left\lfloor n/2\right\rfloor} {2k \choose k}{n \choose 2k}$ . Show that $\sum_{n\geq 0}^{} f(n)x^n=\frac{1}{\sqrt{1-2x-3x^2}}$

Published on 21 Oct 2020 - 13:45

score 66 · Answer 9 · 2020-10-24 22:46:47

66

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$\sum_{n\ge0}f\left(n\right)x^{n}=\frac{1}{\sqrt{1-2x-3x^{2}}}$, where $f(n)$ the $n$-th coefficient of $(1+x+x^2)^n$

Published on 24 Oct 2020 - 22:46

score 41 · Answer 10 · 2026-03-27 10:15:42

41

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Why is it ok to use an equal sign when in analytic continuation

Published on 27 Mar 2026 - 10:15

score 245 · Answer 11 · 2020-11-02 05:46:11

245

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Are generating functions always elements of a ring of formal power series?

Published on 02 Nov 2020 - 5:46

score 63 · Answer 12 · 2020-11-04 07:42:50

63

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Comparing proof of $R[[x]]^$ consists of $\sum_{n \geq 0}a_{n}x^n (a_{n} \in R) ,a_{0} \in R^ ,R$ an integral domain to $R$ a ring.

Published on 04 Nov 2020 - 7:42

score 119 · Answer 13 · 2020-11-05 18:30:24

119

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Proving that the coefficents of the inverse formal power series takes the form $b_{n} = \frac{-1}{a_{0}} (\sum_{i=1}^n a_{i} b_{n-i}). $

Published on 05 Nov 2020 - 18:30

score 577 · Answer 14 · 2020-11-12 01:36:28

577

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Confusion regarding inverse of formal Laurent series

Published on 12 Nov 2020 - 1:36

score 15 · Answer 15 · 2026-03-04 07:03:15

15

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$R=K[[x]]$, show that for every $0\neq f\in R,f|x^n $ and $x^n|f$ where $n\in\mathbb{N}$

Published on 04 Mar 2026 - 7:03

List Question

Question about the computation of a formal power series

Taylor series expansion of $(1+x)^\frac{1}{n}$

Expanding function into formal infinite product

Interchanging $x$ and $y$ in Taylor's Theorem for $f(x+y)$; is there a deeper reason for equality?

How could one port elementary functions to fields of characteristic $p$? Is the concept of a power series similar?

Deriving a power series

How to interpret this q-binomial limit

Let $f(n)=\sum_{k=0}^{\left\lfloor n/2\right\rfloor} {2k \choose k}{n \choose 2k}$ . Show that $\sum_{n\geq 0}^{} f(n)x^n=\frac{1}{\sqrt{1-2x-3x^2}}$

$\sum_{n\ge0}f\left(n\right)x^{n}=\frac{1}{\sqrt{1-2x-3x^{2}}}$, where $f(n)$ the $n$-th coefficient of $(1+x+x^2)^n$

Why is it ok to use an equal sign when in analytic continuation

Are generating functions always elements of a ring of formal power series?

Comparing proof of $R[[x]]^$ consists of $\sum_{n \geq 0}a_{n}x^n (a_{n} \in R) ,a_{0} \in R^ ,R$ an integral domain to $R$ a ring.

Proving that the coefficents of the inverse formal power series takes the form $b_{n} = \frac{-1}{a_{0}} (\sum_{i=1}^n a_{i} b_{n-i}). $

Confusion regarding inverse of formal Laurent series

$R=K[[x]]$, show that for every $0\neq f\in R,f|x^n $ and $x^n|f$ where $n\in\mathbb{N}$

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