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A121225
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Decimal expansion of -log(2-2*cos(1))/2.
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5
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4, 2, 0, 1, 9, 5, 0, 5, 8, 2, 5, 3, 6, 8, 9, 6, 1, 7, 2, 5, 7, 9, 8, 3, 8, 4, 0, 3, 7, 9, 0, 2, 0, 3, 7, 1, 2, 4, 5, 3, 8, 9, 2, 0, 5, 5, 7, 0, 3, 4, 4, 1, 7, 6, 9, 9, 5, 6, 8, 8, 8, 9, 9, 6, 8, 5, 6, 8, 9, 8, 9, 9, 1, 5, 7, 2, 4, 7, 7, 1, 3, 4, 1, 1, 4, 6, 2, 9, 4, 7, 2, 7, 4, 6, 8, 4, 4, 6, 0, 4
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OFFSET
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-1,1
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COMMENTS
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The series Sum_{k>=1} cos(k)/k and also Sum_{k>=1} sin(k)/k (A096444) are called Fresnel series.
Abel summation shows these two series are convergent.
The series Sum_{k>=1} |cos(k)/k| is divergent. (End)
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REFERENCES
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Xavier Merlin, Methodix Analyse, Ellipses, 1997, p. 117.
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LINKS
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FORMULA
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Equals Sum_{k>=1} cos(k)/k.
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EXAMPLE
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0.0420195058253689...
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MATHEMATICA
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RealDigits[N[ -Log[2 - 2 Cos[1]]/2, 101]]
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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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