A175476 Decimal expansion of Pi^(3/2).

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

Offset: 1

Author

R. J. Mathar, May 25 2010

Keywords

• cons
• easy
• nonn

Comments

Log(Pi^(3/2)) = 1.5*log(Pi) = 1.5 * A053510 = 1.7170948...

Examples

			5.5683279968317078452848179..
		

Links

• Marc Chamberland and Armin Straub, On gamma quotients and infinite products, Advances in Applied Mathematics, Vol. 51, No. 5 (2013), pp. 546-562, see pp. 555-556; arXiv preprint, arXiv:1309.3455 [math.NT], 2013, see pp. 9-10.
• Index entries for transcendental numbers.

Crossrefs

Cf. A000796, A002161, A002388, A053510.

Programs

Maple

Pi^(3/2) ; evalf(%) ;

Mathematica

RealDigits[Pi^(3/2), 10, 120][[1]] (* Amiram Eldar, Jun 13 2023 *)

Formula

Equals A000796 * A002161 = A002388 / A002161.

From Vaclav Kotesovec, Dec 10 2015: (Start)

Equals Gamma(3/14)*Gamma(5/14)*Gamma(13/14)/2.

Equals Gamma(1/14)*Gamma(9/14)*Gamma(11/14)/4.

(End)

Equals Integral_{x=-oo..oo, y=-oo..oo, z=-oo..oo} exp(-x^2 - y^2 - z^2) dx dy dz. - Ilya Gutkovskiy, Apr 10 2024