A327996 Decimal expansion of (1/2)*Pi^(3/4)/Gamma(3/4).

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

Offset: 0

Author

Peter Luschny, Oct 24 2019

Keywords

• nonn
• cons

Comments

The function df(x) = 2^(x/2)*(2/Pi)^(sin(Pi*x/2)^2/2)*Gamma(x/2+1) interpolates the double factorials A006882 and extends them analytically. df(1/2) is the given constant. Extending also the notation this can be written as (1/2)!! = Pi^(3/4)/(2*(-1/4)!).

Examples

			Equals 0.962827782446417547919092215448522978271008514478580671...
		

Crossrefs

Cf. A006882, A319332, A327995.

Programs

Maple

Digits := 100: (1/2)*Pi^(3/4)/GAMMA(3/4)*10^86:
ListTools:-Reverse(convert(floor(%), base, 10));

Mathematica

RealDigits[Pi^(3/4)/(2*Gamma[3/4]), 10, 120][[1]] (* Amiram Eldar, May 30 2023 *)

PARI

(1/2)*Pi^(3/4)/gamma(3/4) \\ Michel Marcus, Oct 24 2019

Formula

Equals Pi^(3/4)/(2*(-1/4)!).

From Amiram Eldar, May 30 2023: (Start)

Equals Gamma(1/4)/(2*sqrt(2)*Pi^(1/4)).

Equals A319332 * sqrt(Pi). (End)