A076414 Decimal expansion of first solution of equation cos(x) cosh(x) = 1.

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

Offset: 1

Author

Zak Seidov, Oct 10 2002

Keywords

• easy
• nonn
• cons

Comments

This is an equation related to a beam clumped at both ends: cos(x) cosh(x) = 1. The first three solutions are: 4.73 (this sequence), 7.853 (A076415) and 10.996 (A076416).

Examples

			cos(x) cosh(x) = 1, x = 4.73004.
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 221.

Links

• Z. Guede, I. Elishakov, A fifth-order polynomial that serves as both buckling and vibration mode of an inhomogeneous structure, Chaos, Solitons and Fractals 12 (7) (2001) 1267-1298.

Crossrefs

Cf. A076415, A076416.

Programs

Mathematica

RealDigits[x/.FindRoot[Cos[x] Cosh[x]==1,{x,3 Pi/2},WorkingPrecision -> 120]][[1,1;;105]] (* Jean-Francois Alcover, Mar 14 2011 *)