Apéry's constant: Difference between revisions
Created Nim solution.
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(Created Nim solution.) |
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Apéry's constant via Wedeniwski's summation:
1.2020569031595942853997381615114499907649862923404988817922715553418382057863130901864558736093352581
</pre>
=={{header|Nim}}==
{{trans|Wren}}
{{libheader|bignum}}
<syntaxhighlight lang="Nim">import std/strformat
import bignum
func toDecimal100(r: Rat): string =
## Return the representation of a rational up to 100 decimals.
r *= newInt(10)^100
result.setLen(102)
result = ($r.toInt)[0..100]
result.insert(".", 1)
proc apery(n: Positive) =
var sum = newRat()
for k in 1..n:
sum += newRat(1, k^3)
echo &"First {n} terms of ζ(3) truncated to 100 decimal places (accurate to 6 decimal places):"
echo sum.toDecimal100
echo()
proc markov(n: Positive) =
var neg = true
var fact1, fact2 = newInt(1)
var sum = newRat()
for k in 1..n:
neg = not neg
fact1 *= k
var num = fact1 * fact1
if neg: num = -num
fact2 *= 2 * k * (2 * k - 1)
let denom = fact2 * k^3
sum += newRat(num, denom)
sum *= newRat(5, 2)
echo &"First {n} terms of Markov / Apéry representation truncated to 100 decimal places:"
echo sum.toDecimal100
echo()
proc wedeniwski(n: Positive) =
var fact1, fact2 = newInt(1)
var neg = true
var sum = newRat()
for k in 0..<n:
neg = not neg
if k > 0:
fact1 *= k
fact2 *= 2 * k * (2 * k - 1)
let fact3 = fact2 * (2 * k + 1)
var num = (fact1 * fact2 * fact3)^3
num *= ((((126392 * k + 412708) * k + 531578) * k + 336367) * k + 104000) * k + 12463
if neg: num = -num
let denom = fac(4 * k + 3)^3 * fac(3 * k + 2)
sum += newRat(num, denom)
sum /= 24
echo &"First {n} terms of Wedeniwski representation truncated to 100 decimal places:"
echo sum.toDecimal100
echo()
echo "Actual value to 100 decimal places:"
echo("1.2020569031595942853997381615114499907649862923404988817922715553418382057863130901864558736093352581")
echo()
apery(1000)
markov(158)
wedeniwski(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>
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