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A269063
Decimal expansion of the second inflection point of 1/Gamma(x) on the interval x=[0,infinity).
1
2, 4, 9, 5, 6, 0, 2, 9, 6, 3, 5, 1, 7, 1, 9, 3, 3, 8, 1, 5, 4, 2, 8, 4, 5, 6, 4, 9, 3, 8, 5, 3, 8, 2, 0, 6, 3, 4, 6, 5, 3, 6, 4, 1, 7, 1, 9, 5, 0, 0, 4, 8, 0, 0, 5, 9, 0, 3, 7, 1, 8, 7, 6, 1, 3, 8, 4, 5, 5, 7, 4, 0, 7, 5, 7, 8, 0, 2, 1, 4, 1, 8, 8, 0, 1, 4, 1, 5, 7, 5, 4, 5, 3, 3, 3, 1, 4, 5, 9, 9, 0, 3, 4
OFFSET
1,1
COMMENTS
Also the second positive root of the equation Psi(x)^2-Psi(1,x)=0.
Function 1/Gamma(x) has only two inflection points on the interval x=[0,infinity): 0.30214172... (A268464) and 2.4956029... (this sequence).
EXAMPLE
2.4956029635171933815428456493853820634653641719500480...
MAPLE
Digits:= 150: fsolve(Psi(x)^2-Psi(1, x)=0, x=2.5);
MATHEMATICA
FindRoot[PolyGamma[x]^2-PolyGamma[1, x]==0, {x, 2.5}, WorkingPrecision -> 120][[1, 2]] // RealDigits[#, 10, 103]& // First
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
STATUS
approved