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A233382
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Decimal expansion of the integral over dx/((1+x^2)(1+tan x)) in the limits 0 and Pi/2.
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1
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5, 9, 7, 3, 8, 1, 8, 0, 9, 4, 5, 1, 8, 0, 3, 4, 8, 4, 6, 1, 3, 1, 1, 3, 2, 3, 5, 0, 9, 0, 8, 7, 3, 7, 6, 4, 3, 0, 6, 4, 3, 8, 5, 9, 0, 4, 2, 5, 5, 5, 6, 7, 3, 0, 7, 7, 0, 3, 2, 0, 7, 1, 6, 1, 5, 5, 0, 3, 1, 1, 0, 3, 3, 2, 4, 9, 8, 2, 4, 1, 2, 1, 7, 8, 9, 0, 9, 8, 9, 9, 0, 4, 0, 4, 4, 7, 4, 4, 4, 3, 7, 3, 3, 0, 0, 9
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OFFSET
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0,1
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LINKS
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EXAMPLE
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0.59738180945180348461311323509087376430643859042555673077032071615503110332498…
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MAPLE
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Digits := 60 :
# Expand 1/(1+tan x) in a Taylor series around Pi/4 and exchange
# summation and integration.
for dd from 80 to 100 by 10 do
taylor(1/(1+tan(z)), z=Pi/4, dd) ;
gfun[seriestolist](%) ;
c := evalf(%) ;
x := 0.0 ;
for i from 0 to nops(c)-1 do
1/(1+zz^2)*op(i+1, c)*(zz-Pi/4)^i ;
int(%, zz=0..Pi/2) ;
x := x+evalf(%) ;
end do:
print(x) ;
end do:
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MATHEMATICA
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RealDigits[ NIntegrate[ 1/((1+x^2)(1+Tan[x])), {x, 0, Pi/2}, WorkingPrecision -> 110], 10, 105][[1]] (* Robert G. Wilson v, Sep 29 2014 *)
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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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