A227423 Decimal expansion of 'lambda', a Young-Fejér-Jackson constant linked to the positivity of certain sine sums.

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

Offset

0,1

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 242.

Links

Table of n, a(n) for n=0..100.

Formula

lambda = min { x>0 : (1+x)*Pi - tan(x*Pi) = 0 }.

Example

0.43029665312420275777219844545854836892203153170119392995362943759339439686...

Maple

numdigits:= 120:
lambda:= solve((1+x)*Pi = tan(x*Pi), x):
s:= convert(evalf(lambda, numdigits+10), string):
seq(parse(s[n+1]), n=1..numdigits);  # Alois P. Heinz, Jul 11 2013

Mathematica

lambda /. FindRoot[(1 + lambda)*Pi == Tan[lambda*Pi], {lambda, 2/5}, WorkingPrecision -> 100] // RealDigits // First

Crossrefs

Cf. A227422, A227424, A227425.

Sequence in context: A338149 A338145 A296002 * A199443 A142723 A296228

Adjacent sequences: A227420 A227421 A227422 * A227424 A227425 A227426

Keyword

nonn,cons

Author

Jean-François Alcover, Jul 11 2013

Status

approved