Apéry's constant: Difference between revisions
Added Wren
Thundergnat (talk | contribs) m (→{{header|Raku}}: typoed the typo fix :-( ...) |
(Added Wren) |
||
Line 72:
1.2020569031595942853997381615114499907649862923404988817922715553418382057863130901864558736093352581
</div>
=={{header|Wren}}==
{{libheader|Wren-big}}
<syntaxhighlight lang="ecmascript">import "./big" for BigInt, BigRat
var apery = Fn.new { |n|
var sum = BigRat.zero
for (k in 1..n) sum = sum + BigRat.new(1, k*k*k)
System.print("First %(n) terms of ζ(3) truncated to 100 decimal places (accurate to 6 decimal places):")
System.print(sum.toDecimal(100, false))
System.print()
}
var markov = Fn.new { |n|
var fact = BigInt.one
var fact2 = BigInt.one
var sign = BigInt.minusOne
var sum = BigRat.zero
for (k in 1..n) {
sign = sign * BigInt.minusOne
fact = fact * k
var num = fact.square * sign
var mult = 2 * k * (2*k - 1)
fact2 = fact2 * mult
var cube = k * k * k
var den = fact2 * cube
sum = sum + BigRat.new(num, den)
}
sum = sum * BigRat.new(5, 2)
System.print("First %(n) terms of Markov / Apéry representation truncated to 100 decimal places:")
System.print(sum.toDecimal(100, false))
System.print()
}
var wedeniwski = Fn.new { |n|
var fact = BigInt.one
var fact2 = BigInt.one
var sign = BigInt.minusOne
var sum = BigRat.zero
var mult = 1
for (k in 0..n-1) {
sign = sign * BigInt.minusOne
if (k > 0) {
fact = fact * k
mult = 2 * k * (2*k - 1)
fact2 = fact2 * mult
}
var fact3 = fact2 * (2*k + 1)
var num = sign * fact3.cube * fact2.cube * fact.cube
var cube = k * k * k
var quad = cube * k
var pent = quad * k
var tmp = 126392*pent + 412708*quad + 531578*cube + 336367*k*k + 104000*k + 12463
num = num * tmp
var den = BigInt.factorial(3*k + 2) * BigInt.factorial(4*k + 3).cube
sum = sum + BigRat.new(num, den)
}
sum = sum / 24
System.print("First %(n) terms of Wedeniwski representation truncated to 100 decimal places:")
System.print(sum.toDecimal(100, false))
System.print()
}
System.print("Actual value to 100 decimal places:")
System.print("1.2020569031595942853997381615114499907649862923404988817922715553418382057863130901864558736093352581")
System.print()
apery.call(1000)
markov.call(158)
wedeniwski.call(20)</syntaxhighlight>
{{out}}
<pre>
Actual value to 100 decimal places:
1.2020569031595942853997381615114499907649862923404988817922715553418382057863130901864558736093352581
First 1000 terms of ζ(3) truncated to 100 decimal places (accurate to 6 decimal places):
1.2020564036593442854830714115115999903483212709031775135036540966118572571921400836130084123260473111
First 158 terms of Markov / Apéry representation truncated to 100 decimal places:
1.2020569031595942853997381615114499907649862923404988817922715553418382057863130901864558736093352581
First 20 terms of Wedeniwski representation truncated to 100 decimal places:
1.2020569031595942853997381615114499907649862923404988817922715553418382057863130901864558736093352581
</pre>
| |||