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A364356
Decimal expansion of negative value of function Gamma(-A364355 + i*sqrt(1-A364355^2)).
4
6, 7, 4, 9, 3, 3, 2, 4, 7, 0, 4, 4, 9, 9, 0, 5, 9, 6, 3, 5, 3, 1, 0, 0, 4, 4, 6, 9, 5, 4, 7, 2, 2, 1, 6, 4, 2, 5, 3, 7, 4, 9, 7, 5, 6, 2, 7, 7, 8, 7, 6, 6, 1, 1, 9, 2, 8, 7, 3, 0, 3, 2, 8, 9, 4, 1, 0, 6, 4, 8, 6, 5, 9, 1, 9, 3, 3, 5, 3, 9, 9, 3, 9, 1, 4, 4, 2, 1, 3, 1, 4, 1, 5, 6, 8, 0, 9, 1, 6, 2, 0, 6, 7, 9, 7
OFFSET
0,1
COMMENTS
Only for x = A364355 = 0.54197987169489060244332278779... the Gamma(-x + i*sqrt(1-x^2)) is a real number and -1 < x < 1 (for one case is an imaginary number see A364821 and for other values x is a complex number).
EXAMPLE
Gamma(-A364355 + i*sqrt(1-A364355^2)) = -0.6749332470449905963531...
MATHEMATICA
xmin=x /. FindRoot[Im[Gamma[-x + I Sqrt[1 - x^2]]], {x, 0.5}, WorkingPrecision -> 106]; RealDigits[Re[-Gamma[-x + I Sqrt[1 - x^2]]/. x->xmin]][[1]]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Artur Jasinski, Aug 08 2023
STATUS
approved