A386732 Decimal expansion of Integral_{x>=2} 1/(x^12-1) dx.

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

Offset

0,5

Links

Jason Bard, Table of n, a(n) for n = 0..1003

Michael I. Shamos, A catalog of the real numbers, (2007). See p. 21.

Formula

Equals (1/22528) * hypergeometric(11/12, 1; 23/12; 1/4096).

Equals (-6*Pi - 4*sqrt(3)*Pi + 12*arctan(2) - 3*arctan(12/5) + 6*sqrt(3) * arctan(5/sqrt(3)) + 6*sqrt(3) * arctanh((2*sqrt(3))/5) + log(9261))/72.

Example

0.000044394388389732931619793708861045902941185047688518...

Mathematica

Join[{0, 0, 0, 0}, RealDigits[1/72 (-4 (3 + Sqrt[3]) Pi + 3 (4 ArcTan[2] + 2 Sqrt[3] ArcTan[5/Sqrt[3]] + 2 ArcTan[4 - Sqrt[3]] + 2 ArcTan[4 + Sqrt[3]] + Log[21] - Sqrt[3] Log[5 - 2 Sqrt[3]] + Sqrt[3] Log[5 + 2 Sqrt[3]])), 10, 100][[1]]]
(* or *)
Join[{0, 0, 0, 0}, RealDigits[Integrate[1/(x^12 - 1), {x, 2, Infinity}], 10, 100][[1]]]
(* or *)
Join[{0, 0, 0, 0}, RealDigits[1/22528*Hypergeometric2F1[11/12, 1, 23/12, 1/4096], 10, 100][[1]]]

Crossrefs

Cf. A016644, A105199, A123868, A304656.

Sequence in context: A337365 A345294 A382310 * A233581 A193628 A306506

Adjacent sequences: A386729 A386730 A386731 * A386733 A386734 A386735

Keyword

nonn,cons

Author

Jason Bard, Jul 31 2025

Status

approved