Question

Is there a field extension $E$ of $\mathbb R$ such that every formal power series with coefficients in $\mathbb R$ has a root in $E$?

score 178 · Answer 1 · 2022-10-09 05:08:10

178

Views

Is there a field extension $E$ of $\mathbb R$ such that every formal power series with coefficients in $\mathbb R$ has a root in $E$?

Published on 09 Oct 2022 - 5:08

score 106 · Answer 2 · 2026-03-26 09:27:05

106

Views

Prove that the coefficients of F(x) are positive integers

Published on 26 Mar 2026 - 9:27

score 142 · Answer 3 · 2022-10-14 11:49:05

142

Views

Compute the coefficient of $x^n$

Published on 14 Oct 2022 - 11:49

score 79 · Answer 4 · 2022-10-19 10:03:56

79

Views

$I A[\![X]\!]=I[\![X]\!]$ implies $I$ finitely generated?

Published on 19 Oct 2022 - 10:03

score 31 · Answer 5 · 2026-03-22 05:43:41

31

Views

Infinite series, switched notation, locally finite family of series

Published on 22 Mar 2026 - 5:43

score 39 · Answer 6 · 2026-02-23 13:44:38

39

Views

Is there an accurate representation of Bernoulli umbra?

Published on 23 Feb 2026 - 13:44

score 61 · Answer 7 · 2022-10-25 12:11:29

61

Views

Alternative Proof of Vandermode Convolution

Published on 25 Oct 2022 - 12:11

score 140 · Answer 8 · 2022-10-28 13:12:18

140

Views

The field of formal laurent series viewed as a polynomial ring

Published on 28 Oct 2022 - 13:12

score 149 · Answer 9 · 2026-02-24 08:35:22

149

Views

Prove $\sum_{n \ge 0} (n+1)^{n-1}\frac{x^n}{n!} =(1- \sum_{n \ge 1} (n-1)^{n-1} \frac{x^n}{n!}) ^{-1}$

Published on 24 Feb 2026 - 8:35

score 189 · Answer 10 · 2022-11-02 14:22:30

189

Views

Logarithm is homomorphism

Published on 02 Nov 2022 - 14:22

score 67 · Answer 11 · 2022-11-03 08:24:54

67

Views

Formal power series derivation question

Published on 03 Nov 2022 - 8:24

score 54 · Answer 12 · 2022-11-06 11:01:32

54

Views

Is there a subring of $\overline{\Bbb{Q}_p((t))}=\bigcup_{n\ge 1} \overline{\Bbb{Q}_p}((t^{1/n}))$ that surjects onto $\overline{\Bbb{F}_p((t))}$?

Published on 06 Nov 2022 - 11:01

score 34 · Answer 13 · 2022-11-06 16:54:31

34

Views

Is there an integral formula for the Hadamard product of exponential generating functions?

Published on 06 Nov 2022 - 16:54

score 97 · Answer 14 · 2022-11-09 12:13:23

97

Views

How to prove the compound angle formula rigorously, starting only from the Taylor series definition

Published on 09 Nov 2022 - 12:13

score 112 · Answer 15 · 2022-12-01 15:55:35

112

Views

Formal Powerseries: Compute the reciprocal of $1-A(z)$ for $a_0 \ne 0$

Published on 01 Dec 2022 - 15:55

List Question

Is there a field extension $E$ of $\mathbb R$ such that every formal power series with coefficients in $\mathbb R$ has a root in $E$?

Prove that the coefficients of F(x) are positive integers

Compute the coefficient of $x^n$

$I A[\![X]\!]=I[\![X]\!]$ implies $I$ finitely generated?

Infinite series, switched notation, locally finite family of series

Is there an accurate representation of Bernoulli umbra?

Alternative Proof of Vandermode Convolution

The field of formal laurent series viewed as a polynomial ring

Prove $\sum_{n \ge 0} (n+1)^{n-1}\frac{x^n}{n!} =(1- \sum_{n \ge 1} (n-1)^{n-1} \frac{x^n}{n!}) ^{-1}$

Logarithm is homomorphism

Formal power series derivation question

Is there a subring of $\overline{\Bbb{Q}_p((t))}=\bigcup_{n\ge 1} \overline{\Bbb{Q}_p}((t^{1/n}))$ that surjects onto $\overline{\Bbb{F}_p((t))}$?

Is there an integral formula for the Hadamard product of exponential generating functions?

How to prove the compound angle formula rigorously, starting only from the Taylor series definition

Formal Powerseries: Compute the reciprocal of $1-A(z)$ for $a_0 \ne 0$

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