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A334449
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Decimal expansion of Product_{k>=1} (1 + 1/A002144(k)^5).
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7
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1, 0, 0, 0, 3, 2, 3, 4, 7, 5, 1, 4, 8, 0, 7, 1, 6, 3, 8, 6, 0, 3, 6, 8, 6, 4, 2, 7, 3, 3, 9, 9, 4, 2, 3, 6, 9, 2, 6, 5, 2, 4, 6, 5, 5, 2, 2, 0, 2, 7, 3, 7, 9, 8, 0, 4, 0, 7, 5, 0, 7, 1, 6, 4, 8, 5, 9, 9, 6, 3, 8, 1, 1, 3, 7, 4, 6, 8, 0, 4, 2, 2, 4, 4, 0, 6, 0, 5, 6, 3, 2, 9, 6, 0, 0, 1, 4, 1, 9, 1, 2, 7, 9, 3, 2
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OFFSET
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1,5
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COMMENTS
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In general, for s>0, Product_{k>=1} (1 + 1/A002144(k)^(2*s+1))/(1 - 1/A002144(k)^(2*s+1)) = Pi^(2*s+1) * A000364(s) * zeta(2*s+1) / ((2^(2*s+2) + 2) * (2*s)! * zeta(4*s+2)). - Dimitris Valianatos, May 01 2020
In general, for s>1, Product_{k>=1} (1 + 1/A002144(k)^s)/(1 - 1/A002144(k)^s) = (zeta(s, 1/4) - zeta(s, 3/4)) * zeta(s) / (2^s * (2^s + 1) * zeta(2*s)).
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REFERENCES
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B. C. Berndt, Ramanujan's notebook part IV, Springer-Verlag, 1994, p. 64-65.
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LINKS
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FORMULA
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EXAMPLE
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1.0003234751480716386036864273399423692652465522027379804075071648599638113746...
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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