Question

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

score 118 · Answer 1 · 2026-04-16 05:14:11

118

Views

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

Published on 16 Apr 2026 - 5:14

score 672 · Answer 2 · 2026-04-14 09:56:53

672

Views

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

Published on 14 Apr 2026 - 9:56

score 563 · Answer 3 · 2026-04-16 11:11:39

563

Views

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

Published on 16 Apr 2026 - 11:11

score 165 · Answer 4 · 2026-05-10 15:05:18

165

Views

Cauchy Product $n$ times

Published on 10 May 2026 - 15:05

score 71 · Answer 5 · 2026-04-15 12:10:17

71

Views

Calculate $a_n$ with formal power series

Published on 15 Apr 2026 - 12:10

score 167 · Answer 6 · 2026-05-11 00:31:03

167

Views

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

Published on 11 May 2026 - 0:31

score 54 · Answer 7 · 2026-03-26 01:16:41

54

Views

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

Published on 26 Mar 2026 - 1:16

score 47 · Answer 8 · 2026-03-26 01:16:44

47

Views

Condition for a formal power series to be a Laurent polynomial

Published on 26 Mar 2026 - 1:16

score 45 · Answer 9 · 2026-03-26 01:16:42

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

score 2.3k · Answer 10 · 2026-03-26 01:17:23

2.3k

Views

Polynomial vs power series vs formal power series?

Published on 26 Mar 2026 - 1:17

score 105 · Answer 11 · 2026-05-10 19:23:01

105

Views

Are formal groups associated to various groups different?

Published on 10 May 2026 - 19:23

score 70 · Answer 12 · 2026-03-26 01:17:26

70

Views

Exponential and Natural Log Power Series

Published on 26 Mar 2026 - 1:17

score 47 · Answer 13 · 2026-05-10 18:30:40

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 471 · Answer 14 · 2026-03-26 01:16:46

471

Views

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

Published on 26 Mar 2026 - 1:16

score 51 · Answer 15 · 2026-03-26 01:17:56

51

Views

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

Published on 26 Mar 2026 - 1:17

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

Trending Questions

Popular # Hahtags

Popular Questions