List questions from summability-theory

Published on 03 May 2026 - 3:14

71

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Continuation beyond the natural boundary with $f_+(z)=\lim_{x \to 1-} f(z,x)=\lim_{x \to 1-}\sum_{n=1}^{\infty}\frac{z^{n^2}}{n^n}n^{-n^2 (1-x)} x^n$

Published on 01 May 2026 - 7:15

553

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Where to find a proof of Silverman-Toeplitz?

Published on 06 May 2026 - 20:54

130

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Is the series corresponding to a summable family absolutely convergent?

Published on 24 Apr 2026 - 10:18

90

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If $E$ is a normed $ℝ$-vector space, are we able to show that $(x_i)_{i∈I}⊆E$ is summable $⇔$ $\left(\left\|x_i\right\|_E\right)_{i∈I}$ is summable?

Published on 01 Jun 2017 - 13:23

775

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Proof Silverman-Toeplitz theorem

Published on 25 Mar 2026 - 8:11

707

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A Summability methods which sum the harmonic series

Published on 17 Apr 2026 - 9:31

280

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An oscillating series of real numbers which can be resummed to a complex value

Published on 03 Apr 2026 - 16:32

204

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Integrability with respect to counting measure

Published on 25 Mar 2026 - 8:08

68

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If $\mu$ is a finite measure on a metric space, then for all $\varepsilon$, there is a $\delta<\delta$ with $\mu(\partial B_\delta(x))=0$

Published on 25 Mar 2026 - 8:13

64

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Generalizing Borel Summation to Matrices

Published on 25 Mar 2026 - 8:12

321

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Product of two locally integrable function is locally integrable?

Published on 11 Apr 2026 - 14:24

125

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A question on summable families in topological groups

Published on 25 Mar 2026 - 8:07

List Question

Are the sequences of families for summability or improper summability:

Continuation beyond the natural boundary with $f_+(z)=\lim_{x \to 1-} f(z,x)=\lim_{x \to 1-}\sum_{n=1}^{\infty}\frac{z^{n^2}}{n^n}n^{-n^2 (1-x)} x^n$

Where to find a proof of Silverman-Toeplitz?

Is the series corresponding to a summable family absolutely convergent?

If $E$ is a normed $ℝ$-vector space, are we able to show that $(x_i)_{i∈I}⊆E$ is summable $⇔$ $\left(\left\|x_i\right\|_E\right)_{i∈I}$ is summable?

Proof Silverman-Toeplitz theorem

A Summability methods which sum the harmonic series

An oscillating series of real numbers which can be resummed to a complex value

Integrability with respect to counting measure

If $\mu$ is a finite measure on a metric space, then for all $\varepsilon$, there is a $\delta<\delta$ with $\mu(\partial B_\delta(x))=0$

Generalizing Borel Summation to Matrices

Product of two locally integrable function is locally integrable?

A question on summable families in topological groups

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