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 A233382 Decimal expansion of the integral over dx/((1+x^2)(1+tan x)) in the limits 0 and Pi/2. 1
 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 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS Table of n, a(n) for n=0..105. juantheron, How to evaluate int_0^(pi/2) dx/(1+x^2)/(1+tan x), math.stackexchange, Apr 14 2013 EXAMPLE 0.59738180945180348461311323509087376430643859042555673077032071615503110332498… MAPLE 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: MATHEMATICA 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 *) CROSSREFS Sequence in context: A121060 A230437 A199607 * A021630 A079459 A118309 Adjacent sequences: A233379 A233380 A233381 * A233383 A233384 A233385 KEYWORD cons,less,nonn AUTHOR R. J. Mathar, Dec 08 2013 STATUS approved

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Last modified September 15 10:10 EDT 2024. Contains 375932 sequences. (Running on oeis4.)