A227425 Decimal expansion of 'B', a Young-Fejér-Jackson constant linked to the positivity of certain sine sums.

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

Offset

1,1

References

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

Links

Table of n, a(n) for n=1..101.

Formula

Given lambda from A227423, 'b' is the unique positive solution to (1+lambda)*Pi*((b-1)*psi(1+(b-1)/2)-2*b*psi(1+b/2)+(b+1)*psi(1+(b+1)/2)) = 2*sin(lambda*Pi), where psi is the digamma function.

Example

2.110233966121572196466828156663845189642113029415064842235231216265897058...

Mathematica

b /. FindRoot[(1 + lambda) Pi == Tan[lambda*Pi] && (1 + lambda)*Pi*((b - 1)*PolyGamma[1 + (b - 1)/2] - 2*b*PolyGamma[1 + b/2] + (b + 1) PolyGamma[1 + (b + 1)/2]) == 2*Sin[lambda*Pi], {lambda, 2/5}, {b, 2}, WorkingPrecision -> 105] // RealDigits[#][[1, 1;; 101]&

Crossrefs

Cf. A227422, A227423, A227424.

Sequence in context: A360455 A267486 A285229 * A333213 A301636 A238857

Adjacent sequences: A227422 A227423 A227424 * A227426 A227427 A227428

Keyword

nonn,cons

Author

Jean-François Alcover, Jul 11 2013

Status

approved