A333204 Decimal expansion of arclength from (0,0) to (1,1) on y = x^4.

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

Offset: 1

Author

Clark Kimberling, Jun 12 2020

Keywords

• nonn
• cons
• easy

Examples

			arclength = 1.60022942767220583728997791564995...
		

Crossrefs

Cf. A333202, A333203.

Programs

Mathematica

s = Integrate[Sqrt[1 + 16 x^6], {x, 0, 1}]
r = N[s, 200]
RealDigits[r][[1]]

Formula

arclength = 2F1(-1/2;1/6;7/6;-16), where 2F1 is the hypergeometric function.