List questions from infinite-product

Published on 11 Jan 2024 - 19:37

232

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Show that $e^z-1=z e^{\frac{z}{2}} \prod_{n=1}^{\infty}\left(1+\frac{z^2}{4 n^2 \pi^2}\right)$ using Residue Theorem

Published on 14 Jan 2024 - 21:51

46

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$q$-Pochhammer at root of unity

Published on 25 Mar 2026 - 12:53

68

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$\left(-\frac{1}{2}\right)!$ from the Hypersphere

Published on 27 Mar 2026 - 10:45

75

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Solve an infinite product.

Published on 29 Jan 2024 - 1:22

146

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Cantor's representation of a real as infinite product

Published on 29 Jan 2024 - 20:09

206

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Evaluate the infinite product $ \prod_{n=1}^{\infty} \left ( 1 + \frac{x^2}{n^2+n-1} \right )$

Published on 30 Jan 2024 - 8:00

112

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Does $\prod\limits_{n=1}^{\infty}\int\limits_{-1}^{1}\left|\frac{\lfloor t^{1-n}\rfloor}{\lfloor t^{-n}\rfloor}\right|dt$ converge to $1$?

Published on 03 Feb 2024 - 21:16

117

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Distributive property proof.

Published on 23 Feb 2026 - 13:32

36

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Finding domain of convergence of an infinite product

Published on 10 Feb 2024 - 20:34

306

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Prove that Wallis' product and Euler's formula directly imply that $(-1/2)!=\sqrt{\pi}$

Published on 29 Mar 2026 - 7:19

63

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Completion of an infinite tensor product of Banach spaces: can an infinite product converge to 0?

Published on 21 Feb 2024 - 16:59

69

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How can we formally / rigorously use Mertens' third theorem with $n^2 - 1$ instead of $\ln n$?

Published on 23 Feb 2024 - 14:30

17

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Show $\sum_{n=0}^\infty \frac{(cq^n)_{\infty}}{(bq^n)_{\infty}}=\sum_{m=0}^\infty \frac{(c/b)_mb^mq^{nm}}{(q)_m}$

Published on 26 Mar 2026 - 11:18

105

Views

$\prod_{n=1}^{\infty}(1+e^{-n})=^{?}$ and a series .

Published on 25 Mar 2026 - 23:10

List Question

Evaluate $\prod_{n=2}^\infty(2-2^{1/n})$

Show that $e^z-1=z e^{\frac{z}{2}} \prod_{n=1}^{\infty}\left(1+\frac{z^2}{4 n^2 \pi^2}\right)$ using Residue Theorem

$q$-Pochhammer at root of unity

$\left(-\frac{1}{2}\right)!$ from the Hypersphere

Solve an infinite product.

Cantor's representation of a real as infinite product

Evaluate the infinite product $ \prod_{n=1}^{\infty} \left ( 1 + \frac{x^2}{n^2+n-1} \right )$

Does $\prod\limits_{n=1}^{\infty}\int\limits_{-1}^{1}\left|\frac{\lfloor t^{1-n}\rfloor}{\lfloor t^{-n}\rfloor}\right|dt$ converge to $1$?

Distributive property proof.

Finding domain of convergence of an infinite product

Prove that Wallis' product and Euler's formula directly imply that $(-1/2)!=\sqrt{\pi}$

Completion of an infinite tensor product of Banach spaces: can an infinite product converge to 0?

How can we formally / rigorously use Mertens' third theorem with $n^2 - 1$ instead of $\ln n$?

Show $\sum_{n=0}^\infty \frac{(cq^n)_{\infty}}{(bq^n)_{\infty}}=\sum_{m=0}^\infty \frac{(c/b)_mb^mq^{nm}}{(q)_m}$

$\prod_{n=1}^{\infty}(1+e^{-n})=^{?}$ and a series .

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