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

%I #17 Apr 07 2022 09:21:00

%S 1,2,2,6,1,9,1,1,7,0,8,8,3,5,1,7,0,7,0,8,1,3,0,6,0,9,6,7,4,7,1,9,0,6,

%T 7,5,2,7,2,4,2,4,8,3,5,0,2,2,0,7,4,0,2,7,9,1,3,8,6,1,6,8,4,3,5,4,2,9,

%U 8,4,6,7,6,2,4,4,2,8,0,3,8,1,6,9,2,3,7,4,2,5,6,3,7,7,9,6,6,0,9,5,3,3,4,6,9

%N Decimal expansion of the solution when Gudermannian(x) equals 1.

%C Inverse of A248618.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Gudermannian_function">Gudermannian function</a>.

%F Equals log(tan((2+Pi)/4)). - _Vaclav Kotesovec_, Oct 11 2014

%F From _Amiram Eldar_, Apr 07 2022: (Start)

%F Equals 2*arctanh(tan(1/2)).

%F Equals Integral_{x=0..1} sec(x) dx. (End)

%e 1.22619117088351707081306096747190675272424835022074027913861684354298467624428...

%p evalf(log(tan((2+Pi)/4)),100) # _Vaclav Kotesovec_, Oct 11 2014

%t RealDigits[ InverseGudermannian[ 1], 10, 111][[1]]

%Y Cf. A248618.

%K nonn,cons

%O 1,2

%A _Robert G. Wilson v_, Oct 09 2014