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A227425
Decimal expansion of 'B', a Young-Fejér-Jackson constant linked to the positivity of certain sine sums.
3
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.
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
KEYWORD
nonn,cons
AUTHOR
STATUS
approved