A068353 Decimal expansion of smallest positive root of cos(Pi*x/2)*cosh(Pi*x/2) = -1.

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

Offset: 1

Author

Joost de Winter, Feb 28 2002

Keywords

• nonn
• cons

Examples

			1.1937283253889343234388...
		

Links

• E. A. Harrington, The vibrations of tuning-forks, J. Opt. Soc. Am., 17, 224-237 (1928).
• G. H. Keulegan, On the vibration of U bars, Doctoral dissertation, Johns Hopkins University, 1928.
• A. M. Liebetrau, Some tests of randomness based upon the variance-time curve of the Poisson process Journal of the Royal Statistical Society, Series B (Methodological), 41, September 1979, 32-39.

Crossrefs

Equals (2/Pi) times A076417.

Programs

Mathematica

RealDigits[FindRoot[Cos[Pi x/2]Cosh[Pi x/2]==-1, {x, 1}, WorkingPrecision->200][[1, 2]]][[1]]

PARI

solve(x=1,2,cos(x)*cosh(x)+1)*2/Pi \\ Charles R Greathouse IV, Apr 16 2014

Extensions

Edited by Dean Hickerson, Jun 07 2002

Offset corrected by R. J. Mathar, Feb 05 2009