Apéry's constant: Difference between revisions

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: