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

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

Offset: 1

Author

Clark Kimberling, Jul 03 2020

Keywords

• nonn
• cons

Comments

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.

Crossrefs

Cf. A335929.

Programs

Mathematica

r = NIntegrate[Sqrt[1 + D[Gamma[x], x]^2], {x, 1, 2}, WorkingPrecision -> 200]
RealDigits[r][[1]]
Plot[Gamma[x] - 1, {x, .5, 2.5}]