Apéry's constant: Difference between revisions
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1.2020569031595942853997381615114499907649862923404988817922715553418382057863130901864558736093352581
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=={{header|Julia}}==
<syntaxhighlight lang="julia">using SpecialFunctions
setprecision(120, base=10)
println("Apéry's constant via Julia's zeta:\n$(string(zeta(big"3"))[1:102])")
""" zeta(3) via Riemann summation of 1/(k cubed) """
Apéry_r(nterms = 1_000_000) = sum(big"1" / k^big"3" for k in 1:nterms)
println("\nApéry's constant via reciprocal cubes:\n$(string(Apéry_r())[1:102])")
""" zeta(3) via Markov's summation """
function Apéry_m(nterms = 158)
return big"2.5" * sum((isodd(k) ? 1 : -1) * factorial(big(k))^2 /
(factorial(big"2" * k) * k^big"3") for k in 1:nterms)
end
println("\nApéry's constant via Markov's summation:\n$(string(Apéry_m())[1:102])")
""" zeta(3) via Wedeniwski's summation """
function Apéry_w(nterms = 20)
return big"1"/24 * sum((iseven(k) ? 1 : -1) * factorial(big"2" * k + 1)^3 *
factorial(big"2" * k)^3 * factorial(big(k))^3 *
(126392 * k^big"5" + 412708 * k^big"4" + 531578 * k^big"3" + 336367 * k^big"2"
+ big"104000" * k + 12463) / (factorial(big"3" * k + 2) * factorial(big"4" * k+3)^3)
for k in 0:nterms)
end
println("\nApéry's constant via Wedeniwski's summation:\n$(string(Apéry_w())[1:102])")
</syntaxhighlight>{{out}}
<pre>
Apéry's constant via Julia's zeta:
1.2020569031595942853997381615114499907649862923404988817922715553418382057863130901864558736093352581
Apéry's constant via reciprocal cubes:
1.2020569031590942858997379115114499908483196256737488817922717053418382053696464235214344450378979367
Apéry's constant via Markov's summation:
1.2020569031595942853997381615114499907649862923404988817922715553418382057863130901864558736093352581
Apéry's constant via Wedeniwski's summation:
1.2020569031595942853997381615114499907649862923404988817922715553418382057863130901864558736093352581
</pre>
=={{header|Phix}}==
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