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%I #8 Jun 14 2020 22:47:05
%S 5,8,6,9,5,6,0,3,7,7,3,4,7,6,1,4,3,9,4,0,8,8,1,7,2,5,6,8,1,9,2,8,4,8,
%T 6,4,0,7,9,7,0,2,7,6,0,0,9,8,0,0,9,6,7,2,2,4,0,8,1,2,3,5,9,7,2,4,9,9,
%U 5,0,5,2,2,1,2,9,9,2,6,9,1,3,9,9,5,2,6
%N Decimal expansion of the real part of the complex root of cos(x + i*y) = x + i*y with least x > 0 and y > 0.
%H Henry E. Fettis, <a href="https://www.jstor.org/stable/2005324">Complex Roots of sin z = az, cos z = az, and cosh z = az</a>, Mathematics of Computation, Vol. 30, No. 135 (1976), pp. 541-545, Table 18, <a href="https://doi.org/10.1090/S0025-5718-1976-0418401-9">alternative link</a> (without the tables).
%H T. H. Miller, <a href="http://dx.doi.org/10.1017/S0013091500030868">On the numerical values of the roots of the equation cos x = x</a>, Proc. Edinburgh Math. Soc., Vol. 9 (1890), pp. 80-83.
%H T. Hugh Miller, <a href="https://doi.org/10.1017/S001309150003460X">On the imaginary roots of cos x = x</a>, Proc. Edinburgh Math. Soc., Vol. 21 (1902), pp. 160-162 (the last 3 pages of the pdf file).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DottieNumber.html">Dottie Number</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Dottie_number">Dottie number</a>.
%e 5.86956037734761439408817256819284864079702760098009...
%t z = {x, y} /. FindRoot[{x == Cos[x]*Cosh[y], y == -Sin[x]*Sinh[y]}, {{x, 5}, {y, 2}}, WorkingPrecision -> 100]; RealDigits[z[[1]], 10, 90][[1]]
%Y Cf. A003957, A335563, A335564, A335566 (the imaginary part).
%K nonn,cons
%O 1,1
%A _Amiram Eldar_, Jun 14 2020
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