

A367309


Decimal expansion of area under the curve (12^(1x))*zeta(x) from 0 to 1.


4



6, 0, 2, 1, 1, 2, 3, 4, 9, 3, 1, 0, 3, 7, 1, 5, 5, 4, 9, 7, 1, 1, 2, 6, 3, 2, 0, 0, 5, 1, 5, 4, 1, 3, 5, 9, 9, 4, 8, 4, 7, 1, 2, 0, 0, 0, 0, 0, 6, 3, 9, 4, 6, 5, 9, 6, 7, 3, 6, 5, 2, 6, 3, 5, 8, 3, 0, 8, 2, 6, 8, 1, 4, 1, 8, 7, 7, 3, 7, 5, 7, 1, 8, 5, 6, 4
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OFFSET

0,1


COMMENTS

The series Sum_{n >= 1} (1)^(n+1)/n^x converges nonuniformly to g(x) = (1  2^(1x))*zeta(x) on the open interval (0, 1). This series can be described as an alternating version of the 'pseries' when 0 < p < 1. Let f(x) = Sum_{n >= 1} (1)^(n+1)/n^x. Then f(0+) = g(0) = 1/2 and f(1) = log(2), whereas g(1) is undefined, but has the limit value log(2). Also, f(1/2) = g(1/2) = A113024 = 0.604898643421... .


LINKS



EXAMPLE

0.60211234931037155497112632...


MATHEMATICA

y = NIntegrate[(1  2^(1x)) Zeta[x], {x, 0, 1}, WorkingPrecision > 200]
RealDigits[y][[1]]


PROG

(PARI) intnum(x=0, 1, (12^(1x))*zeta(x)) \\ Michel Marcus, Nov 14 2023


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



