A335565 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.

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, 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, 5, 0, 5, 2, 2, 1, 2, 9, 9, 2, 6, 9, 1, 3, 9, 9, 5, 2, 6

Offset

1,1

Links

Table of n, a(n) for n=1..87.

Henry E. Fettis, Complex Roots of sin z = az, cos z = az, and cosh z = az, Mathematics of Computation, Vol. 30, No. 135 (1976), pp. 541-545, Table 18, alternative link (without the tables).

T. H. Miller, On the numerical values of the roots of the equation cos x = x, Proc. Edinburgh Math. Soc., Vol. 9 (1890), pp. 80-83.

T. Hugh Miller, On the imaginary roots of cos x = x, Proc. Edinburgh Math. Soc., Vol. 21 (1902), pp. 160-162 (the last 3 pages of the pdf file).

Eric Weisstein's World of Mathematics, Dottie Number.

Wikipedia, Dottie number.

Example

5.86956037734761439408817256819284864079702760098009...

Mathematica

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]]

Crossrefs

Cf. A003957, A335563, A335564, A335566 (the imaginary part).

Sequence in context: A322633 A346443 A145432 * A365793 A070371 A199444

Adjacent sequences: A335562 A335563 A335564 * A335566 A335567 A335568

Keyword

nonn,cons

Author

Amiram Eldar, Jun 14 2020

Status

approved