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Search: id:A100554
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| A100554 |
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Decimal expansion of the fractional part of Sum[Cos[(n + 1)*Pi]*Zeta[2*n], {n, 1, Infinity}] = Zeta[2] - Zeta[4] + Zeta[6] - Zeta[8] + ..., where Zeta is the Riemann zeta function. |
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+0
2
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| 5, 7, 6, 6, 7, 4, 0, 4, 7, 4, 6, 8, 5, 8, 1, 1, 7, 4, 1, 3, 4, 0, 5, 0, 7, 9, 4, 7, 5, 0, 0, 0, 0, 4, 9, 0, 4, 4, 5, 6, 5, 6, 2, 6, 6, 4, 0, 3, 8, 1, 6, 6, 6, 5, 5, 7, 5, 0, 6, 2, 4, 8, 4, 3, 9, 0, 1, 5, 4, 2, 4, 7, 9, 1, 8, 3, 1, 0, 0, 2, 1, 7, 4, 3, 5, 6, 5, 5, 5, 1, 7, 5, 9, 3, 9, 5, 4, 9, 1, 8, 7, 6, 5, 1, 7
(list; cons; graph; listen)
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OFFSET
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0,1
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COMMENT
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For odd upper bounds, the sum converges to the given value p in (0,1) with no fractional part function necessary. For even upper bounds, the sum converges to p+1.
Decimal expansion of (psi(i)-psi(-i))/2/i-3/2 where psi is the digamma function - Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 28 2004
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EXAMPLE
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0.576674047468581174134050794750000490...
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MATHEMATICA
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N[FractionalPart[Sum[Cos[(n + 1)*Pi]*Zeta[2*n], {n, 1, 500}]], 140] N[FractionalPart[Sum[Cos[(n + 1)*Pi]*Zeta[2*n], {n, 1, 1000}]], 140]
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PROGRAM
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(PARI) (psi(I)-psi(-I))/2/I-3/2
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CROSSREFS
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Adjacent sequences: A100551 A100552 A100553 this_sequence A100555 A100556 A100557
Sequence in context: A063005 A059249 A114603 this_sequence A138306 A001620 A101456
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KEYWORD
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cons,nonn
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AUTHOR
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Joseph Biberstine (jrbibers(AT)indiana.edu), Nov 27 2004
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