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A084233
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Decimal expansion of area under the curve Zeta(1/2 + t*I) from zero to its first nontrivial zero (A058303).
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0
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1, 3, 8, 3, 2, 8, 5, 3, 0, 4, 2, 2, 7, 2, 2, 5, 1, 8, 8, 5, 6, 6, 8, 3, 0, 2, 5, 4, 8, 2, 9, 4, 6, 9, 8, 3, 9, 3, 2, 7, 0, 0, 6, 8, 2, 8, 4, 8, 5, 1, 9, 9, 2, 2, 3, 9, 9, 8, 0, 4, 9, 3, 3, 3, 6, 7, 4, 4, 5, 0, 3, 0, 3, 9, 8, 6, 4, 2, 0, 0, 6, 0, 3, 1, 4, 8, 9, 5, 6, 0, 2, 6, 2, 5, 9, 0, 5, 7, 4, 6
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 2,2
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LINKS
| Eric Weisstein's World of Mathematics, Riemann Zeta Function Zeros
Index entries for zeta function.
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EXAMPLE
| 13.832853042...
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MATHEMATICA
| NIntegrate[ Re[ Zeta[1/2 + t*I ]], {t, 0, Re[ FindRoot[ Zeta[1/2 + t*I], {t, 14 + {-.3, +.3}}] [[1, 2]]]}, AccuracyGoal -> 120, WorkingPrecision -> 150 ]
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PROG
| (PARI) intnum(t=0, solve(s=14, 15, imag(zeta(1/2+I*s))), abs(zeta(1/2+I*t))) [From Brad Chalfan (brad(AT)chalfan.net), Aug 31 2010]
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CROSSREFS
| Cf. A058303.
Sequence in context: A021727 A021265 A115369 * A198489 A015136 A179450
Adjacent sequences: A084230 A084231 A084232 * A084234 A084235 A084236
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KEYWORD
| nonn,cons
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AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com), May 11 2003
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EXTENSIONS
| More terms and PARI program from Brad Chalfan (brad(AT)chalfan.net), Aug 31 2010
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