Question

What are the exact limits of validity of the Abel-Plana summation formula?

score 405 · Answer 1 · 2026-03-25 07:44:45

405

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What are the exact limits of validity of the Abel-Plana summation formula?

Published on 25 Mar 2026 - 7:44

score 34 · Answer 2 · 2026-03-25 09:24:59

34

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Finding a combined function from infinite series with a function in it

Published on 25 Mar 2026 - 9:24

score 27 · Answer 3 · 2026-03-25 07:48:38

27

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what will be the $(t+1)$-th term in this summation expansion and why?

Published on 25 Mar 2026 - 7:48

score 134 · Answer 4 · 2026-04-23 21:51:12

134

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Do Divergent Integrals have a unique regularisation?

Published on 23 Apr 2026 - 21:51

score 95 · Answer 5 · 2026-04-10 17:06:50

95

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Prove the combinatorial identity

Published on 10 Apr 2026 - 17:06

score 192 · Answer 6 · 2026-03-25 11:04:47

192

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$ \sum_{n = 1}^{\infty} ( \frac{p_{2n-1}}{p_{2n}} - \frac{p_{2n}}{p_{2n +1}} ) = ?? $

Published on 25 Mar 2026 - 11:04

score 52 · Answer 7 · 2026-03-25 07:45:35

52

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How is $\sum_{k \geq 0} \sum_{i \geq k+1} \mathbb{P}(X=i) = \sum_{i \geq 1} \sum_{k=0}^{i-1}\mathbb{P}(X=i) = \sum_{i \geq1} i \mathbb{P}(X=i) $?

Published on 25 Mar 2026 - 7:45

score 2.2k · Answer 8 · 2026-03-25 11:03:28

2.2k

Views

On proving that $\sum\limits_{n=1}^\infty \frac{n^{13}}{e^{2\pi n}-1}=\frac 1{24}$

Published on 25 Mar 2026 - 11:03

score 161 · Answer 9 · 2026-03-25 09:32:07

161

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Estimate on partial sum $\sum_{n=1}^x \frac{\sin^2(n)}{n}$ using Abel Plana Summation Formula :

Published on 25 Mar 2026 - 9:32

score 166 · Answer 10 · 2026-03-25 07:45:35

166

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Show $\sum_{n \in \mathbb{Z}} \sum_{k \in \mathbb{Z}} a_k b_{n-k} z^n =(\sum_{n \in \mathbb{Z}}a_n z^n)(\sum_{n \in \mathbb{Z}}b_n z^n)$

Published on 25 Mar 2026 - 7:45

score 190 · Answer 11 · 2026-03-25 11:04:42

190

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A closed form for $\sum_{k=0}^n \frac{ (-1)^k {n \choose k}^2}{k+1}$

Published on 25 Mar 2026 - 11:04

score 111 · Answer 12 · 2026-05-10 19:25:19

111

Views

$\sum_{(s,t)\in S\times T} f(s,t)=\sum_{s\in S}\sum_{t\in T} f(s,t)$ via Fubini-Tonelli?

Published on 10 May 2026 - 19:25

score 30 · Answer 13 · 2026-03-25 07:40:30

30

Views

Closed form expression for the following Binomial expansion

Published on 25 Mar 2026 - 7:40

score 8.9k · Answer 14 · 2026-03-25 07:45:56

8.9k

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Towards a new proof of infinitude of primes ( with possible unified application to other primes of special forms whose Infinitude is unknown):

Published on 25 Mar 2026 - 7:45

score 35 · Answer 15 · 2026-03-25 07:47:25

35

Views

Decreasing summation amount based on number selected

Published on 25 Mar 2026 - 7:47

List Question

What are the exact limits of validity of the Abel-Plana summation formula?

Finding a combined function from infinite series with a function in it

what will be the $(t+1)$-th term in this summation expansion and why?

Do Divergent Integrals have a unique regularisation?

Prove the combinatorial identity

$ \sum_{n = 1}^{\infty} ( \frac{p_{2n-1}}{p_{2n}} - \frac{p_{2n}}{p_{2n +1}} ) = ?? $

How is $\sum_{k \geq 0} \sum_{i \geq k+1} \mathbb{P}(X=i) = \sum_{i \geq 1} \sum_{k=0}^{i-1}\mathbb{P}(X=i) = \sum_{i \geq1} i \mathbb{P}(X=i) $?

On proving that $\sum\limits_{n=1}^\infty \frac{n^{13}}{e^{2\pi n}-1}=\frac 1{24}$

Estimate on partial sum $\sum_{n=1}^x \frac{\sin^2(n)}{n}$ using Abel Plana Summation Formula :

Show $\sum_{n \in \mathbb{Z}} \sum_{k \in \mathbb{Z}} a_k b_{n-k} z^n =(\sum_{n \in \mathbb{Z}}a_n z^n)(\sum_{n \in \mathbb{Z}}b_n z^n)$

A closed form for $\sum_{k=0}^n \frac{ (-1)^k {n \choose k}^2}{k+1}$

$\sum_{(s,t)\in S\times T} f(s,t)=\sum_{s\in S}\sum_{t\in T} f(s,t)$ via Fubini-Tonelli?

Closed form expression for the following Binomial expansion

Towards a new proof of infinitude of primes ( with possible unified application to other primes of special forms whose Infinitude is unknown):

Decreasing summation amount based on number selected

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