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A227422
Decimal expansion of a Young-Fejér-Jackson constant linked to the nonnegativity of certain cosine sums.
3
4, 5, 6, 7, 8, 0, 1, 8, 8, 2, 6, 0, 7, 2, 6, 7, 0, 7, 0, 1, 6, 0, 3, 7, 0, 8, 3, 8, 2, 5, 5, 4, 1, 1, 0, 8, 9, 7, 0, 6, 8, 0, 2, 6, 0, 1, 8, 8, 1, 9, 7, 2, 2, 4, 9, 8, 8, 3, 7, 7, 2, 2, 0, 2, 9, 4, 5, 5, 0, 8, 5, 2, 9, 0, 7, 1, 7, 3, 8, 7, 2, 2, 9, 8, 6, 7, 8, 8, 1, 4, 7, 4, 2, 3, 0, 5, 0, 7, 5, 9
OFFSET
1,1
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 242.
FORMULA
min { x : 9*x^7+55*x^6-14*x^5-948*x^4-3247*x^3-5013*x^2-3780*x-1134 = 0 }.
EXAMPLE
4.56780188260726707016037083825541108970680260188197224988377220294550852907...
MAPLE
Digits:= 132:
fsolve(9*x^7+55*x^6-14*x^5-948*x^4-3247*x^3-5013*x^2-3780*x-1134, x, 4..5):
s:= convert(%/10, string):
seq(parse(s[n+1]), n=1..Digits-10); # Alois P. Heinz, Jul 11 2013
MATHEMATICA
x /. NSolve[ 9x^7 + 55x^6 - 14x^5 - 948x^4 - 3247x^3 - 5013x^2 - 3780x - 1134, x, WorkingPrecision -> 100] // Last // RealDigits[#, 10, 100] & // First
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
STATUS
approved