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A227424 Decimal expansion of 'mu', a Young-Fejér-Jackson constant linked to the positivity of certain sine sums. 3
8, 1, 2, 8, 2, 5, 2, 4, 2, 1, 0, 5, 5, 0, 7, 2, 6, 0, 7, 6, 0, 0, 8, 7, 1, 2, 3, 1, 1, 8, 3, 7, 0, 2, 9, 8, 6, 4, 7, 0, 1, 0, 1, 3, 4, 0, 5, 2, 8, 7, 0, 3, 4, 0, 6, 5, 7, 3, 6, 0, 0, 3, 9, 5, 8, 0, 7, 2, 7, 4, 7, 2, 6, 7, 9, 4, 0, 2, 2, 7, 2, 3, 8, 3, 9, 1, 2, 5, 2, 9, 4, 7, 9, 0, 9, 6, 4, 6, 7, 2, 9, 8, 2 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

REFERENCES

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

LINKS

Table of n, a(n) for n=0..102.

FORMULA

Given lambda from A227423, mu is the unique positive solution of (1+lambda)*sin(mu*Pi) = mu*sin(lambda*Pi).

EXAMPLE

0.81282524210550726076008712311837029864701013405287034065736003958072747...

MAPLE

Digits:= 127:

lambda:= solve((1+x)*Pi - tan(x*Pi), x):

mu:= fsolve((1+lambda)*sin(x*Pi)-x*sin(lambda*Pi), x, 0.1..1):

s:= convert(mu, string):

seq(parse(s[n+1]), n=1..Digits-10);  # Alois P. Heinz, Jul 11 2013

MATHEMATICA

mu /. FindRoot[(1 + lambda)*Pi == Tan[lambda*Pi] && (1 + lambda)*Sin[mu*Pi] == mu* Sin[lambda*Pi], {lambda, 2/5}, {mu, 4/5}, WorkingPrecision -> 100] // RealDigits // First

CROSSREFS

Cf. A227422, A227423, A227425.

Sequence in context: A154167 A140242 A156944 * A248965 A266152 A021127

Adjacent sequences:  A227421 A227422 A227423 * A227425 A227426 A227427

KEYWORD

nonn,cons

AUTHOR

Jean-François Alcover, Jul 11 2013

STATUS

approved

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Last modified December 18 23:46 EST 2018. Contains 318245 sequences. (Running on oeis4.)