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A335960 Decimal expansion of the arclength for Gamma(x) for 1 < x < 2. 1

%I #4 Jul 04 2020 01:45:46

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

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

%U 2,6,5,5,1,4,4,0,4,6,4,8,3,7,5,3,3,2

%N Decimal expansion of the arclength for Gamma(x) for 1 < x < 2.

%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.

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

%t RealDigits[r][[1]]

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

%Y Cf. A335929.

%K nonn,cons

%O 1,3

%A _Clark Kimberling_, Jul 03 2020

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