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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 July 15 22:48 EDT 2019. Contains 325061 sequences. (Running on oeis4.)