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