Question

Why no one uses the product formula for sine function to calculate $\pi$?

score 109 · Answer 1 · 2026-03-29 11:02:15

109

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Why no one uses the product formula for sine function to calculate $\pi$?

Published on 29 Mar 2026 - 11:02

score 20 · Answer 2 · 2024-03-29 05:19:54

20

Views

Functional Equation for Holomorphic Infinite Product

Published on 29 Mar 2024 - 5:19

score 117 · Answer 3 · 2026-03-29 10:49:06

117

Views

How to show$\frac{\pi}{4} = \frac{2\cdot4\cdot4\cdot6\cdot6\cdot8 \dotsm}{3\cdot3\cdot5\cdot5\cdot7\cdot7 \dotsm}$?

Published on 29 Mar 2026 - 10:49

score 160 · Answer 4 · 2015-01-11 12:58:16

160

Views

How to evaluate the product:

Published on 11 Jan 2015 - 12:58

score 484 · Answer 5 · 2015-01-14 23:15:03

484

Views

Limit of product with prime numbers

Published on 14 Jan 2015 - 23:15

score 589 · Answer 6 · 2015-01-18 12:45:45

589

Views

$\prod\limits_{k = 0}^\infty {(1 - {p_k})} = 0$ if and only if $\sum\limits_{k = 0}^\infty {{p_k}} $ diverges

Published on 18 Jan 2015 - 12:45

score 735 · Answer 7 · 2015-01-19 09:19:06

735

Views

Inequality $\prod\limits_{r=1}^{\infty}\left(1+\frac{1}{2^r}\right)<\frac 52$

Published on 19 Jan 2015 - 9:19

score 708 · Answer 8 · 2015-01-22 02:35:29

708

Views

How can I find the sum of an infinite series of products?

Published on 22 Jan 2015 - 2:35

score 212 · Answer 9 · 2015-01-25 09:56:25

212

Views

convergence of $(1+\frac{1}{2})(1+\frac{1}{4})\cdots(1+\frac{1}{2^n})$

Published on 25 Jan 2015 - 9:56

score 118 · Answer 10 · 2015-01-25 18:59:24

118

Views

a question concerning infinite product

Published on 25 Jan 2015 - 18:59

score 172 · Answer 11 · 2015-01-26 07:05:33

172

Views

show that $e=(\frac{2}{1})^{\frac{1}{1}}(\frac{4}{3})^{\frac{1}{2}}(\frac{6\cdot8}{5\cdot7})^{\frac{1}{4}}...$

Published on 26 Jan 2015 - 7:05

score 63 · Answer 12 · 2015-01-27 06:11:35

63

Views

Show that: $\lim_{n \to \infty}\prod_{k=1}^n \cos(k\sqrt{\frac{3}{n^3}} t) = e^{- \frac{t^2}{2}}$

Published on 27 Jan 2015 - 6:11

score 512 · Answer 13 · 2015-01-30 01:19:53

512

Views

Divergent products.

Published on 30 Jan 2015 - 1:19

score 69 · Answer 14 · 2015-02-10 03:59:37

69

Views

Find the values of x for which $\sum_{n=0}^\infty (-\frac{1}{2})^n(x-3)^n$ converges

Published on 10 Feb 2015 - 3:59

score 254 · Answer 15 · 2015-02-10 19:14:19

254

Views

Evaluation of $\lim_{x \to k\pi} \frac{\sin(x)}{x(x-k\pi)}$ from the Weierstrass product expansion of $\sin(x)$

Published on 10 Feb 2015 - 19:14

List Question

Why no one uses the product formula for sine function to calculate $\pi$?

Functional Equation for Holomorphic Infinite Product

How to show$\frac{\pi}{4} = \frac{2\cdot4\cdot4\cdot6\cdot6\cdot8 \dotsm}{3\cdot3\cdot5\cdot5\cdot7\cdot7 \dotsm}$?

How to evaluate the product:

Limit of product with prime numbers

$\prod\limits_{k = 0}^\infty {(1 - {p_k})} = 0$ if and only if $\sum\limits_{k = 0}^\infty {{p_k}} $ diverges

Inequality $\prod\limits_{r=1}^{\infty}\left(1+\frac{1}{2^r}\right)<\frac 52$

How can I find the sum of an infinite series of products?

convergence of $(1+\frac{1}{2})(1+\frac{1}{4})\cdots(1+\frac{1}{2^n})$

a question concerning infinite product

show that $e=(\frac{2}{1})^{\frac{1}{1}}(\frac{4}{3})^{\frac{1}{2}}(\frac{6\cdot8}{5\cdot7})^{\frac{1}{4}}...$

Show that: $\lim_{n \to \infty}\prod_{k=1}^n \cos(k\sqrt{\frac{3}{n^3}} t) = e^{- \frac{t^2}{2}}$

Divergent products.

Find the values of x for which $\sum_{n=0}^\infty (-\frac{1}{2})^n(x-3)^n$ converges

Evaluation of $\lim_{x \to k\pi} \frac{\sin(x)}{x(x-k\pi)}$ from the Weierstrass product expansion of $\sin(x)$

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