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

1,1

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).

References

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

Links

Table of n, a(n) for n=1..105.

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.

Example

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

Mathematica

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

Crossrefs

Cf. A076415, A076416.

Sequence in context: A341813 A088446 A362253 * A198574 A098233 A200602

Adjacent sequences: A076411 A076412 A076413 * A076415 A076416 A076417

Keyword

easy,nonn,cons

Author

Zak Seidov, Oct 10 2002

Status

approved