List questions from formal-power-series

Published on 15 Oct 2018 - 22:04

166

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Find the sum of $1-\frac17+\frac19-\frac1{15}+\frac1{17}-\frac1{23}+\frac1{25}-\dots$

Published on 25 Mar 2026 - 1:18

296

Views

Uniqueness in Weierstraß p-adic preparation theorem

Published on 13 Nov 2018 - 14:21

1.4k

Views

Why $K[[X]]$ is PID and what's the form of the ring's ideals?

Published on 13 Nov 2018 - 22:56

171

Views

Exponentiate generating functions as formal power series

Published on 16 Nov 2018 - 5:41

80

Views

Preimage of a prime ideal in a ring of formal power series.

Published on 11 Dec 2018 - 22:30

59

Views

Any identity (involving addition, multiplication, substitution) between real/complex power series is an identity in the ring of formal power series.

Published on 01 Jan 2019 - 14:39

426

Views

How to show that $\gcd(a_1,a_2,\cdots,a_k) = 1$ implies that there exist a non-negative solution to $\sum_{i=1}^{n}a_ix_i = n$ for large $n.$

Published on 25 Mar 2026 - 8:58

71

Views

Show that $e^{\frac{-\hbar}{2}\partial_{a}\partial_{b}}e^{\frac{-ab}{\hbar}}=2e^{\frac{-2ab}{\hbar}}$

Published on 25 Mar 2026 - 6:12

192

Views

Determining solutions for convergence of formal power series

Published on 23 Jan 2019 - 18:13

236

Views

On integral closedness of formal power series ring over an integrally closed domain satisfying Krull intersection principle

Published on 23 Feb 2026 - 2:31

136

Views

On $A$ algebra homomorphisms $A[[X_1,...,X_n]]\to Q(A)$, where $A$ is a complete DVR

Published on 25 Mar 2026 - 14:25

133

Views

Transferring big Witt vectors from "power series form" to "vector form"

Published on 20 Feb 2019 - 15:14

1.7k

Views

Spectrum of the ring of formal power series over integers

Published on 28 Feb 2019 - 12:44

127

Views

Proving that the given element is irreducible but not prime

Published on 05 Mar 2019 - 7:49

List Question

What is a common framework for these divergent sums?

Find the sum of $1-\frac17+\frac19-\frac1{15}+\frac1{17}-\frac1{23}+\frac1{25}-\dots$

Uniqueness in Weierstraß p-adic preparation theorem

Why $K[[X]]$ is PID and what's the form of the ring's ideals?

Exponentiate generating functions as formal power series

Preimage of a prime ideal in a ring of formal power series.

Any identity (involving addition, multiplication, substitution) between real/complex power series is an identity in the ring of formal power series.

How to show that $\gcd(a_1,a_2,\cdots,a_k) = 1$ implies that there exist a non-negative solution to $\sum_{i=1}^{n}a_ix_i = n$ for large $n.$

Show that $e^{\frac{-\hbar}{2}\partial_{a}\partial_{b}}e^{\frac{-ab}{\hbar}}=2e^{\frac{-2ab}{\hbar}}$

Determining solutions for convergence of formal power series

On integral closedness of formal power series ring over an integrally closed domain satisfying Krull intersection principle

On $A$ algebra homomorphisms $A[[X_1,...,X_n]]\to Q(A)$, where $A$ is a complete DVR

Transferring big Witt vectors from "power series form" to "vector form"

Spectrum of the ring of formal power series over integers

Proving that the given element is irreducible but not prime

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