login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Decimal expansion of second solution of equation cos(x) cosh(x) = 1.
2

%I #10 Mar 30 2012 17:26:04

%S 7,8,5,3,2,0,4,6,2,4,0,9,5,8,3,7,5,5,6,4,7,7,0,6,6,6,8,7,2,5,4,0,4,9,

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

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

%N Decimal expansion of second solution of equation cos(x) cosh(x) = 1.

%C This is an equation related to a beam clumped at both ends: cos(x) cosh(x) = 1. The first three solutions are: 4.73 (A076414), 7.853 (this sequence) and 10.996 (A076416).

%H Z. Guede, I. Elishakov, <a href="http://dx.doi.org/10.1016/S0960-0779(00)00014-X">A fifth-order polynomial that serves as both..</a>, Chaos, Solitons and Fractals 12 (2001) 1267-1298.

%e cos(x) cosh(x) = 1, x = 7.8532...

%t RealDigits[x/.FindRoot[Cos[x] Cosh[x]==1,{x,5 Pi/2},WorkingPrecision->120]][[1]] (* Jean-Francois Alcover, Mar 14 2011 *)

%Y Cf. A076414, A076416.

%K easy,nonn,cons

%O 1,1

%A _Zak Seidov_, Oct 10 2002