Question

How to prove that this infinite product of continued fractions converges to $1-\frac{1}{z}$?

score 289 · Answer 1 · 2026-03-28 21:34:13

289

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How to prove that this infinite product of continued fractions converges to $1-\frac{1}{z}$?

Published on 28 Mar 2026 - 21:34

score 308 · Answer 2 · 2016-02-24 18:14:51

308

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Infinite products of even analytic functions - highly accurate approximation

Published on 24 Feb 2016 - 18:14

score 91 · Answer 3 · 2016-02-27 20:40:08

91

Views

Can one define an uncountable infinite product?

Published on 27 Feb 2016 - 20:40

score 1k · Answer 4 · 2016-02-29 15:47:17

1k

Views

Euler's Basel problem proof explanation

Published on 29 Feb 2016 - 15:47

score 445 · Answer 5 · 2016-02-29 21:19:47

445

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Infinite Earring and Product Space Homeomorphic

Published on 29 Feb 2016 - 21:19

score 2.5k · Answer 6 · 2016-03-02 01:58:46

2.5k

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Examples where series converges but product diverges and vice versa

Published on 02 Mar 2016 - 1:58

score 153 · Answer 7 · 2026-03-27 15:36:08

153

Views

Uniform and absolute convergence of infinite trigonometric product

Published on 27 Mar 2026 - 15:36

score 128 · Answer 8 · 2016-03-02 02:51:31

128

Views

Simple questions about infinite products

Published on 02 Mar 2016 - 2:51

score 276 · Answer 9 · 2016-03-03 20:19:42

276

Views

Closed form for $\prod_{n=0}^\infty (1-z^{2^n})$

Published on 03 Mar 2016 - 20:19

score 1k · Answer 10 · 2016-03-10 22:04:22

1k

Views

Closed form for the infinite product $\prod\limits_{k=0}^{\infty} \left( 1-x^{2^k} \right)$

Published on 10 Mar 2016 - 22:04

score 375 · Answer 11 · 2026-03-30 11:40:08

375

Views

Find $\lim\limits_{n\to\infty}{\left(1+\frac{1}{n^k}\right)\left(1+\frac{2}{n^k}\right)\cdots\left(1+\frac{n}{n^k}\right) }$ for $k=1, 2, 3, \cdots$

Published on 30 Mar 2026 - 11:40

score 38 · Answer 12 · 2016-03-17 18:11:50

38

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If $\prod _{n = 1 }^{\infty} a_n = 0$, then $lim_{n \rightarrow \infty} a_n = 0$ or $\exists n$ : $a_n =0$?

Published on 17 Mar 2016 - 18:11

score 326 · Answer 13 · 2016-03-19 01:17:51

326

Views

Complex Finite Product $\prod_{k=0}^{n-1} (1-\zeta^k z)$

Published on 19 Mar 2016 - 1:17

score 245 · Answer 14 · 2016-03-20 00:41:16

245

Views

Constructing a smooth function whose roots consist only of each of the primes.

Published on 20 Mar 2016 - 0:41

score 268 · Answer 15 · 2016-03-21 01:49:33

268

Views

Proof that these two expressions are equivalent

Published on 21 Mar 2016 - 1:49

List Question

How to prove that this infinite product of continued fractions converges to $1-\frac{1}{z}$?

Infinite products of even analytic functions - highly accurate approximation

Can one define an uncountable infinite product?

Euler's Basel problem proof explanation

Infinite Earring and Product Space Homeomorphic

Examples where series converges but product diverges and vice versa

Uniform and absolute convergence of infinite trigonometric product

Simple questions about infinite products

Closed form for $\prod_{n=0}^\infty (1-z^{2^n})$

Closed form for the infinite product $\prod\limits_{k=0}^{\infty} \left( 1-x^{2^k} \right)$

Find $\lim\limits_{n\to\infty}{\left(1+\frac{1}{n^k}\right)\left(1+\frac{2}{n^k}\right)\cdots\left(1+\frac{n}{n^k}\right) }$ for $k=1, 2, 3, \cdots$

If $\prod _{n = 1 }^{\infty} a_n = 0$, then $lim_{n \rightarrow \infty} a_n = 0$ or $\exists n$ : $a_n =0$?

Complex Finite Product $\prod_{k=0}^{n-1} (1-\zeta^k z)$

Constructing a smooth function whose roots consist only of each of the primes.

Proof that these two expressions are equivalent

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