A076415 -id:A076415 - cp's OEIS frontend

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

Zak Seidov, Oct 10 2002

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).

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

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

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.

Cf. A076415, A076416.

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

A076416 Decimal expansion of third solution of equation cos(x)*cosh(x) = 1.

Original entry on oeis.org

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

Offset: 2

Zak Seidov, Oct 10 2002

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 (A076415) and 10.9956 (this sequence).

			10.995607838001670906669...

Z. Guede and 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.

Cf. A076414, A076415.

RealDigits[x/.FindRoot[Cos[x] Cosh[x]==1,{x,7 Pi/2},WorkingPrecision -> 120]][[1]] (* Jean-François Alcover, Mar 14 2011 *)

solve(x=9,11,cos(x)*cosh(x)-1) \\ Charles R Greathouse IV, Mar 15 2011

Offset corrected by R. J. Mathar, Feb 05 2009

cp's OEIS Frontend

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

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