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
Jean-François Alcover, Jul 11 2013
STATUS
approved