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January 24, 2026 16:26
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Wallis product in Haskell - https://en.wikipedia.org/wiki/Wallis_product
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| import Data.Ratio | |
| rat f g r = f (numerator r) % g (denominator r) | |
| num f = rat f id | |
| den f = rat id f | |
| -- fun way | |
| wallis = (2 % 1) : zipWith ($) (cycle [den (+2), num (+2)]) wallis | |
| -- direct way | |
| wallis' = map (\n -> (4 * n**2) % (4 * n**2 - 1)) [1..] | |
| -- >>> pi/2 | |
| -- 1.5707963267948966 | |
| -- >>> fromRational $ product $ take 10000 wallis | |
| -- 1.5707177967949542 |
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