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A333972
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Decimal expansion of Pi^6/540 = zeta(2) * zeta(4).
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3
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1, 7, 8, 0, 3, 5, 0, 3, 5, 8, 4, 7, 2, 7, 8, 5, 9, 9, 4, 5, 0, 0, 4, 0, 6, 3, 7, 7, 1, 3, 4, 1, 1, 0, 9, 2, 3, 8, 2, 8, 1, 8, 0, 6, 0, 7, 5, 5, 7, 4, 9, 3, 7, 3, 3, 2, 2, 4, 2, 1, 5, 1, 6, 2, 0, 0, 7, 5, 8, 1, 3, 2, 0, 0, 7, 8, 4, 2, 6, 3, 2, 1, 2, 9, 4, 8, 5, 4, 4, 6, 1, 3, 9, 2, 4
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OFFSET
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1,2
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COMMENTS
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Compare 1st formula with Sum_{m>0, q>0} 1/(m^2*q^2) = Pi^4/36 = (zeta(2))^2 = A098198.
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REFERENCES
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Jean-Marie Monier, Analyse, Exercices corrigés, 2ème année MP, Dunod, 1997, Exercice 3.22, p. 275.
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LINKS
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FORMULA
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Equals Sum_{m>0, q>0, m | q} 1/(m^2*q^2).
Equals Sum_{k>=1} sigma_2(k)/k^4. - Amiram Eldar, Sep 30 2020
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EXAMPLE
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1.78035035847278599450040637713411092382818060755749373322421516...
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MAPLE
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evalf(Pi^6/540, 120);
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MATHEMATICA
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RealDigits[Pi^6/540, 10, 100][[1]] (* Amiram Eldar, Sep 29 2020 *)
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PROG
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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