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Decimal expansion of the area of the region bounded by y = 1 and y = Gamma(x).
8

%I #4 Jul 04 2020 01:45:01

%S 0,7,7,2,5,4,0,4,9,3,1,9,3,6,9,3,9,4,8,5,6,1,1,9,5,1,7,6,5,4,2,4,4,4,

%T 2,2,5,6,2,7,6,5,6,0,8,2,8,9,3,1,4,0,8,4,7,9,7,9,1,9,5,9,1,6,4,6,1,5,

%U 0,9,4,1,3,4,8,0,2,4,2,1,7,2,4,1,1,6,2

%N Decimal expansion of the area of the region bounded by y = 1 and y = Gamma(x).

%C Gamma(1) = Gamma(2) = 1, and the interval (1,2) gives the portion of the graph of y = Gamma x that lies under the line y = 1, as shown by the Mathematica program.

%e area = 0.07725404931936939485611951765424442256276560828931408...

%t r = NIntegrate[1 - Gamma[x], {x, 1, 2}, WorkingPrecision -> 200]

%t RealDigits[r][[1]]

%t Plot[Gamma[x] - 1, {x, .5, 2.5}]

%Y Cf. A335960.

%K nonn,cons

%O 0,2

%A _Clark Kimberling_, Jul 03 2020