A152584 Decimal expansion of (Pi^3)/24.

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

Offset: 1

Author

Eric Desbiaux, Dec 08 2008

Keywords

• cons
• nonn

Comments

Consider infinite sum made of areas of circles Pi*radius^2 with diameter 1/n.

The volume is (Pi/4)*(1 + 1/4 + 1/9 + 1/16 + 1/25 + ... + 1/n^2)

= (1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + ...)*(1 + 1/4 + 1/9 + 1/16 + 1/25 + ...)

= (Pi/4) * (Pi^2/6) = Pi^3/24.

Equals volume of a cone of height Pi^2/8 and radius 1.

Equals volume of a sphere (4*Pi*Pi^2/32)/3 with radius^3 = (Pi^2/32).

Examples

			1.291928195012492507311513127795891466759387023578...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000
• Index entries for transcendental numbers

Crossrefs

Cf. A013661, A003881, A102753, A019679, A111003.

Programs

Mathematica

RealDigits[(Pi^3)/24, 10, 50][[1]] (* G. C. Greubel, Jun 09 2017 *)

PARI

(Pi^3)/24 \\ G. C. Greubel, Jun 09 2017

Formula

Equals Integral_{x=0..oo} arctan(x)^2/(x^2 + 1) dx. - Amiram Eldar, Aug 06 2020