A076418 -id:A076418 - cp's OEIS frontend

A076417 Decimal expansion of first solution of equation cos(x)*cosh(x) = -1.

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

Offset: 1

Zak Seidov, Oct 10 2002

This is an equation related to a cantilever beam: cos(x)*cosh(x) = -1. The first three solutions are: 1.875 (this sequence), 4.69409 (A076418) and 7.854757 (A076419).

			1.87510406871196116644530824107821416257011173353...

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. A009398, A076418, A076419.

Cf. A005981, A058258, A008775.

RealDigits[x/.FindRoot[Cos[x]Cosh[x]==-1,{x,1.8}, WorkingPrecision->120], 10,120][[1]] (* Harvey P. Dale, Jul 24 2011 *)

solve(x=1, 2, cos(x)*cosh(x) + 1) \\ Michel Marcus, Sep 11 2019

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

Original entry on oeis.org

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

Zak Seidov, Oct 10 2002

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).

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

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. A076417, A076418.

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

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

cp's OEIS Frontend

A076417 Decimal expansion of first solution of equation cos(x)*cosh(x) = -1.

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