login
A376643
Decimal expansion 4*EllipticK(4/5)/sqrt(5), where EllipticK is the complete elliptic integral of the first kind.
0
4, 0, 3, 7, 8, 1, 1, 6, 3, 9, 9, 5, 6, 8, 4, 6, 4, 3, 1, 1, 6, 8, 0, 2, 8, 8, 7, 9, 9, 9, 7, 8, 6, 4, 9, 3, 0, 1, 3, 6, 0, 8, 3, 9, 9, 3, 4, 0, 8, 8, 0, 6, 8, 5, 7, 8, 6, 3, 4, 9, 6, 1, 5, 9, 8, 9, 7, 7, 7, 3, 8, 3, 7, 8, 6, 5, 3, 1, 9, 4, 7, 4, 4, 4, 0, 7, 7, 0, 1, 5, 0, 7, 0, 3, 3, 7, 9, 1, 9, 6, 9, 1, 0, 5, 7
OFFSET
1,1
COMMENTS
A point mass is attached to a frictionless pivot by a massless string of length L and revolves in a vertical circle about the pivot in a uniform gravitational field with an acceleration g. The slowest possible motion occurs when the tension in the string is momentarily zero at the top of the route, and the longest-possible period is then c * sqrt(L/g), where c is this constant.
FORMULA
Equals 2 * Integral_{0..Pi} (1/sqrt(3 + 2*cos(x))) dx.
EXAMPLE
4.03781163995684643116802887999786493013608399340880...
MATHEMATICA
RealDigits[4 * EllipticK[4/5] / Sqrt[5], 10, 120][[1]]
PROG
(PARI) 4*ellK(sqrt(4/5))/sqrt(5)
CROSSREFS
Constants related to similar physical problems: A019692, A038533, A038534, A175574, A256514, A309893, A310000.
Sequence in context: A352718 A338736 A281531 * A248914 A373462 A246686
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Oct 01 2024
STATUS
approved