A220610 Decimal expansion of sqrt(2*Pi^3).

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

Offset: 1

Author

Bruno Berselli, Dec 25 2012

Keywords

• nonn
• cons

Comments

This is the case n=4 of Product_{i=1..n-1} Gamma(i/n) = sqrt((2*Pi)^(n-1)/n).

Continued fraction expansion: 7, 1, 6, 1, 79, 4, 7, 1, 1, 1, 1, 1, 1, 4, 2, 3, 73, 1, 2, 1, 14, 3, 2, 1, 1, 2, 3, 1, ...

Examples

			7.8748049728612098721453229972336022711558426913993669291...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Wikipedia, Particular values of the Gamma function: Products
• Index entries for transcendental numbers

Crossrefs

Cf. numbers of the form sqrt((2*Pi)^(n-1)/n) -- see the first comment: A002161 (n=2), A186706 (n=3).

Programs

Magma

SetDefaultRealField(RealField(100)); R:= RealField(); Sqrt(2*Pi(R)^3); // G. C. Greubel, Sep 29 2018

Maple

evalf(sqrt(2*Pi^3),120); # Muniru A Asiru, Sep 30 2018

Mathematica

RealDigits[Sqrt[2 Pi^3], 10, 90][[1]]

Maxima

fpprec:90; ev(bfloat(sqrt(2*%pi^3)));

PARI

default(realprecision, 100); sqrt(2*Pi^3) \\ G. C. Greubel, Sep 29 2018

Formula

Equals A002193*A175476.