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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 (list; constant; graph; refs; listen; history; text; internal format)
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: A123340 A267486 A285229 * A301636 A238857 A253587

Adjacent sequences:  A227422 A227423 A227424 * A227426 A227427 A227428

KEYWORD

nonn,cons

AUTHOR

Jean-François Alcover, Jul 11 2013

STATUS

approved

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Last modified November 16 03:41 EST 2018. Contains 317252 sequences. (Running on oeis4.)