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A248618 Decimal expansion of the solution when inverse Gudermannian(x) equals 1.

%I A248618 #27 Apr 07 2022 09:21:27
%S A248618 8,6,5,7,6,9,4,8,3,2,3,9,6,5,8,6,2,4,2,8,9,6,0,1,8,4,6,1,9,1,8,4,4,4,
%T A248618 4,1,3,7,9,6,7,9,1,9,9,2,4,8,7,6,0,0,9,9,6,1,1,8,4,8,2,2,9,7,4,2,4,4,
%U A248618 8,2,2,9,4,5,8,4,1,7,0,2,8,2,0,9,9,2,0,9,2,3,6,4,0,4,8,5,7,2,7,4,1,4,6,5,2
%N A248618 Decimal expansion of the solution when inverse Gudermannian(x) equals 1.
%C A248618 Inverse of A248617.
%C A248618 This is the angle of the unique wedge having its apex at the origin and kissing the exponential curve y=exp(x) on one side, and its inverse logarithmic function y=log(x) on the other side. - _Stanislav Sykora_, May 31 2015
%H A248618 Stanislav Sykora, <a href="/A248618/b248618.txt">Table of n, a(n) for n = 0..2000</a>
%H A248618 Wikipedia, <a href="http://en.wikipedia.org/wiki/Gudermannian_function">Gudermannian function</a>.
%F A248618 Equals arcsin((exp(2)-1)/(exp(2)+1)). - _Vaclav Kotesovec_, Oct 11 2014
%F A248618 Equals atan(e)-atan(1/e) = A257777-A258428. - _Stanislav Sykora_, May 31 2015
%F A248618 From _Amiram Eldar_, Apr 07 2022: (Start)
%F A248618 Equals 2*arctan(tanh(1/2)).
%F A248618 Equals Integral_{x=0..1} sech(x) dx. (End)
%e A248618 0.86576948323965862428960184619184444137967919924876009961184822974244822945841...
%e A248618 The wedge angle in degrees:
%e A248618 49.6049374208547003776513077348112118247866748819092710723979907940346891648208... - _Stanislav Sykora_, May 31 2015
%p A248618 evalf(arcsin((exp(2)-1)/(exp(2)+1)),100) # _Vaclav Kotesovec_, Oct 11 2014
%t A248618 RealDigits[ Gudermannian[ 1], 10, 111][[1]]
%o A248618 (PARI) asin((exp(2)-1)/(exp(2)+1)) \\ _Michel Marcus_, Oct 11 2014
%o A248618 (PARI) atan(exp(1))-atan(1/exp(1)) \\ _Stanislav Sykora_, May 31 2015
%o A248618 (PARI) 2*atan(exp(1))-Pi/2 \\ _Charles R Greathouse IV_, Jun 02 2015
%Y A248618 Cf. A248617, A257777, A258428.
%K A248618 nonn,cons
%O A248618 0,1
%A A248618 _Robert G. Wilson v_, Oct 09 2014