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Ramanujan's constant: Difference between revisions
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NB. approximation as a rational number
]RC=: +`%/ }: 1j1 (#!.1) 262537412640768743 1 1333462407511 1 8 1 1 5 1 4 1 7 1 1 1 9 1 1 2 12 4 1 15 4 299 3 5 1 4 5 5 1 28 3 1 9 4 1 6 1 1 1 1 1 1 51 11 5 3 2 1 1 1 1 2 1 5 1 9 1x
45120712325606158012363304056579024470785114628332049030433r171863933112440071790625667019825998411698
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NB. returns u to at least y significant digits▼
Digits=: adverb define NB. u Digits y u y is less accurate than u y+1
▲ NB. returns u to at least y significant digits
format=. ' _.' -.~ ((j.~ 50&+) y)&":
i =. 5
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)
cf=: 0.1&$: :(4 :0) NB. tolerance cf value -> continued fraction approximation of value to tolerance
whilst. X < | approximation - y do.
'term Y' =. <.`([:%1&|)`:0 Y
terms =. terms , term
approximation =. +`%/ }: 1j1 #!.1 terms
end.
)
assert (-: 0&cf) 649r200
assert 13r4 (-: cf) 649r200
NB. pi is sufficiently fast for partial series recomputation.
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exp=: (1x"_)`((($:~<:)+^%!@x:@])~)@.(0<[) NB. recursive Taylor series x exp y recursively sums x terms of Taylor series for Exp[y], memoization candidate.
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NB. takes the constant beyond the repeat 9s.
S=: cf_sqrt&163 Digits 34
P=: pi Digits 34
Y=:
f=: exp&Y M. NB. memoize
59j40 ": 8 ^~ f Digits 34
262537412640768743.
NB. ^
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