Question

Showing that $\exp(\sum_{n=1}^\infty a_nX^n)=\prod_{n=1}^\infty\exp(a_nX^n)$ for formal power series

score 115 · Answer 1 · 2014-08-27 11:15:31

115

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Showing that $\exp(\sum_{n=1}^\infty a_nX^n)=\prod_{n=1}^\infty\exp(a_nX^n)$ for formal power series

Published on 27 Aug 2014 - 11:15

score 669 · Answer 2 · 2014-09-30 11:28:18

669

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motivation for $1/(1-x)$ used in generating functions

Published on 30 Sep 2014 - 11:28

score 560 · Answer 3 · 2014-11-25 23:38:46

560

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$\frac{1}{x^2} \int xe^x dx$ without using integration by parts

Published on 25 Nov 2014 - 23:38

score 161 · Answer 4 · 2014-11-27 01:45:35

161

Views

Cauchy Product $n$ times

Published on 27 Nov 2014 - 1:45

score 68 · Answer 5 · 2014-12-07 09:49:40

68

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Calculate $a_n$ with formal power series

Published on 07 Dec 2014 - 9:49

score 161 · Answer 6 · 2026-03-25 14:22:52

161

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Why formal power series are not considered a system of hypercomplex numbers?

Published on 25 Mar 2026 - 14:22

score 53 · Answer 7 · 2019-10-02 17:38:18

53

Views

What kinds of expressions have a self-similar open form?

Published on 02 Oct 2019 - 17:38

score 46 · Answer 8 · 2019-10-02 19:31:43

46

Views

Condition for a formal power series to be a Laurent polynomial

Published on 02 Oct 2019 - 19:31

score 44 · Answer 9 · 2019-10-12 22:12:41

$\mathbb{C}\left(z\right)\left[\left[w\right]\right]\cap\mathbb{C}\left(w\right)\left[\left[z\right]\right]\overset{?}{=}\mathbb{C}\left(z,w\right)$

score 2.3k · Answer 10 · 2019-10-15 16:56:14

2.3k

Views

Polynomial vs power series vs formal power series?

Published on 15 Oct 2019 - 16:56

score 97 · Answer 11 · 2019-10-17 06:02:54

97

Views

Are formal groups associated to various groups different?

Published on 17 Oct 2019 - 6:02

score 69 · Answer 12 · 2019-10-19 12:00:46

69

Views

Exponential and Natural Log Power Series

Published on 19 Oct 2019 - 12:00

score 40 · Answer 13 · 2026-03-25 17:15:43

Can we consider formal power series $P(t)=\sum_{m=0}^{\infty} \binom{2m}{m} \left[m^l(4t-1)^l+F_l(t) \right]t^m$ as formal group law?

score 470 · Answer 14 · 2019-10-22 10:32:32

470

Views

Generalizing the Weierstrass Preparation Theorem to formal power series in multiple variables

Published on 22 Oct 2019 - 10:32

score 50 · Answer 15 · 2019-10-27 10:01:37

50

Views

Prove that $(1 + z)^x \cdot (1+z)^y = (1+z)^{(x+y)}$ for formal power series

Published on 27 Oct 2019 - 10:01

List Question

Showing that $\exp(\sum_{n=1}^\infty a_nX^n)=\prod_{n=1}^\infty\exp(a_nX^n)$ for formal power series

motivation for $1/(1-x)$ used in generating functions

$\frac{1}{x^2} \int xe^x dx$ without using integration by parts

Cauchy Product $n$ times

Calculate $a_n$ with formal power series

Why formal power series are not considered a system of hypercomplex numbers?

What kinds of expressions have a self-similar open form?

Condition for a formal power series to be a Laurent polynomial

$\mathbb{C}\left(z\right)\left[\left[w\right]\right]\cap\mathbb{C}\left(w\right)\left[\left[z\right]\right]\overset{?}{=}\mathbb{C}\left(z,w\right)$

Polynomial vs power series vs formal power series?

Are formal groups associated to various groups different?

Exponential and Natural Log Power Series

Can we consider formal power series $P(t)=\sum_{m=0}^{\infty} \binom{2m}{m} \left[m^l(4t-1)^l+F_l(t) \right]t^m$ as formal group law?

Generalizing the Weierstrass Preparation Theorem to formal power series in multiple variables

Prove that $(1 + z)^x \cdot (1+z)^y = (1+z)^{(x+y)}$ for formal power series

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