A076419 Decimal expansion of third solution of equation cos(x)*cosh(x) = -1.

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

Offset: 1

Author

Zak Seidov, Oct 10 2002

Keywords

• easy
• nonn
• cons

Comments

This is an equation related to a cantilever beam: cos(x)*cosh(x) = -1. The first three solutions are: 1.875 (A076417), 4.69409 (A076418) and 7.854757 (this sequence).

Examples

			cos(x) cosh(x) = -1, x = 7.854757...
		

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. A076417, A076418.

Programs

Mathematica

RealDigits[x/.FindRoot[Cos[x]Cosh[x]==-1,{x,8},WorkingPrecision-> 120]] [[1]] (* Harvey P. Dale, Oct 17 2021 *)

PARI

solve(x=7, 8, cos(x)*cosh(x) + 1) \\ Michel Marcus, Sep 11 2019