The OEIS is supported by the many generous donors to the OEIS Foundation.
Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #16 May 02 2023 02:26:09
%S 7,0,6,8,5,8,2,7,4,5,6,2,8,7,3,2,0,8,8,5,5,2,9,5,8,9,2,7,5,4,6,6,6,5,
%T 3,7,6,4,3,7,6,4,7,5,5,0,0,6,4,2,3,5,6,4,4,0,5,9,4,3,7,7,5,4,3,4,5,0,
%U 1,3,4,3,0,5,6,6,0,8,6,9,3,9,5,4,0,8,4,7,5,2,6,1,5,2,2,3,6,6,0,8,3,8,2,0,4
%N Decimal expansion of second solution to tan(x) = tanh(x).
%C This is an equation related to a beam clamped at left and simply supported at right: tan(x) = tanh(x). The first three solutions are: 3.927... (A076420), 7.0686... (this sequence) and 10.21... (A076422).
%H Zakoua Guédé and Isaac Elishakoff, <a href="http://dx.doi.org/10.1016/S0960-0779(00)00014-X">A fifth-order polynomial that serves as both buckling and vibration mode of an inhomogeneous structure</a>, Chaos, Solitons and Fractals 12 (7) (2001) 1267-1298.
%e 7.06858274562873208855295892754666537643764755006423...
%t RealDigits[x /. FindRoot[Tan[x] == Tanh[x], {x, 7}, WorkingPrecision->120], 10, 105][[1]] (* _Amiram Eldar_, May 02 2023 *)
%o (PARI) solve(x = 7, 7.1, tan(x) - tanh(x)) \\ _Amiram Eldar_, May 02 2023
%Y Cf. A076420, A076422.
%K easy,nonn,cons
%O 1,1
%A _Zak Seidov_, Oct 10 2002