A233382 Decimal expansion of the integral over dx/((1+x^2)(1+tan x)) in the limits 0 and Pi/2.

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

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