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A013671
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Decimal expansion of zeta(13).
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22
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1, 0, 0, 0, 1, 2, 2, 7, 1, 3, 3, 4, 7, 5, 7, 8, 4, 8, 9, 1, 4, 6, 7, 5, 1, 8, 3, 6, 5, 2, 6, 3, 5, 7, 3, 9, 5, 7, 1, 4, 2, 7, 5, 1, 0, 5, 8, 9, 5, 5, 0, 9, 8, 4, 5, 1, 3, 6, 7, 0, 2, 6, 7, 1, 6, 2, 0, 8, 9, 6, 7, 2, 6, 8, 2, 9, 8, 4, 4, 2, 0, 9, 8, 1, 2, 8, 9, 2, 7, 1, 3, 9, 5, 3, 2, 6, 8, 1, 3
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OFFSET
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1,6
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REFERENCES
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 811.
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LINKS
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
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FORMULA
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Definition: zeta(13) = sum {n >= 1} 1/n^13.
zeta(13) = 2^13/(2^13 - 1)*( sum {n even} n^9*p(n)*p(1/n)/(n^2 - 1)^14 ), where p(n) = n^6 + 21*n^4 + 35*n^2 + 7. (End)
zeta(13) = Sum_{n >= 1} (A010052(n)/n^(13/2)) = Sum_{n >= 1} ( (floor(sqrt(n))-floor(sqrt(n-1)))/n^(13/2) ). - Mikael Aaltonen, Feb 22 2015
zeta(13) = Product_{k>=1} 1/(1 - 1/prime(k)^13). - Vaclav Kotesovec, May 02 2020
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EXAMPLE
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1.0001227133475784891467518365263573957142751058955098451367026716208967...
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MATHEMATICA
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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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