A103430 Decimal expansion of integral(1/(n*log(n))^(3/2),n=2..Inf).
6, 8, 3, 2, 1, 8, 5, 9, 7, 1, 7, 6, 0, 4, 7, 3, 8, 2, 1, 7, 9, 3, 2, 0, 3, 9, 0, 3, 0, 1, 9, 5, 2, 6, 6, 2, 8, 9, 4, 0, 0, 7, 6, 5, 2, 1, 8, 6, 9, 7, 7, 4, 4, 9, 9, 5, 1, 1, 5, 4, 0, 4, 7, 6, 9, 1, 8, 3, 5, 1, 5, 6, 8, 4, 1, 8, 5, 2, 8, 0, 0, 0, 5, 9, 6, 2, 8, 4, 9, 6, 7, 9, 0, 7, 3, 3, 8, 3, 1, 8, 1, 1, 0, 7, 5
Offset: 0
Examples
0.6832185971760473821793203903019526628940076521...
Links
- G. C. Greubel, Table of n, a(n) for n = 0..10000
Crossrefs
Cf. A103359.
Programs
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Mathematica
(2 - Erfc[Sqrt[Log[2]/2]]*Sqrt[Pi*Log[16]])/Sqrt[Log[4]] // RealDigits[#, 10, 105]& // First (* Jean-François Alcover, Feb 19 2013 *)
Formula
Integral(1/(n*log(n))^(3/2), n=2..inf) = sqrt(2)(1/sqrt(log 2) - sqrt(Pi)*erfc(sqrt(log(2)/2))).
Extensions
Typo in formula fixed by Jean-François Alcover, Feb 19 2013
Comments