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A076421
Decimal expansion of second solution to tan(x) = tanh(x).
2
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, 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, 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
OFFSET
1,1
COMMENTS
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).
LINKS
Zakoua Guédé and Isaac Elishakoff, 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
7.06858274562873208855295892754666537643764755006423...
MATHEMATICA
RealDigits[x /. FindRoot[Tan[x] == Tanh[x], {x, 7}, WorkingPrecision->120], 10, 105][[1]] (* Amiram Eldar, May 02 2023 *)
PROG
(PARI) solve(x = 7, 7.1, tan(x) - tanh(x)) \\ Amiram Eldar, May 02 2023
CROSSREFS
Sequence in context: A021590 A094241 A021938 * A196763 A321106 A225457
KEYWORD
easy,nonn,cons
AUTHOR
Zak Seidov, Oct 10 2002
STATUS
approved