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A225122
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Numerators of Integral_{x=0..Pi/2} sin(2*n*x)*log(cosec(x)) dx.
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2
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0, 1, 1, 7, 1, 43, 23, 337, 22, 1091, 563, 12701, 1627, 172673, 88069, 179141, 5692, 3141493, 1593269, 61309987, 7759469, 8966941, 31730711, 1474162241, 93044486, 7510486741, 3788707301, 22918154531, 2888008157, 675037481999, 340028535787
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OFFSET
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0,4
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COMMENTS
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The integral with sin(2*n*x) is always rational, but the integral with sin((2*n+1)*x) is irrational and is of the form p/q+log(2)/(2*n+1).
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REFERENCES
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George Boros and Victor H. Moll, Irresistible integrals, Cambridge University Press (2006), p. 218.
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LINKS
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EXAMPLE
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0, 1/2, 1/2, 7/18, 1/3, 43/150, 23/90, 337/1470, 22/105, 1091/5670, 563/3150, ... = A225122/A225123
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MAPLE
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a:= n-> numer(Re(int(sin(2*n*x)*log(csc(x)), x=0..Pi/2))):
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MATHEMATICA
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a[n_] := Integrate[Sin[2*n*x]*Log[Csc[x]], {x, 0, Pi/2}]; Table[a[n] // Numerator, {n, 0, 30}]
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CROSSREFS
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KEYWORD
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nonn,easy,frac
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AUTHOR
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STATUS
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approved
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