A347430 Simple continued fraction expansion of Pi^(3/2)/Gamma(3/4)^2.

3, 1, 2, 2, 2, 1, 8, 1, 2, 1, 2, 9, 8, 6, 56, 5, 38, 1, 2, 1, 5, 1, 5, 1, 2, 10, 3, 10, 741, 1, 5, 3, 3, 1, 5, 2, 3, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 7, 2, 3, 3, 4, 4, 1, 11, 1, 2, 1, 1, 1, 1, 1, 5, 1, 64, 1, 1, 2, 7, 1, 5, 98, 2, 2, 2, 1, 1, 1, 1, 1, 5, 1, 3, 1

Offset: 0

Author

Adam Filinovich, Sep 01 2021

Keywords

• nonn
• cofr

Examples

			3+1/(1+1/(2+1/(2+1/(2+...)))).
		

Links

• M. Parker, What is the area of a Squircle?, Youtube video (2021).
• Eric Weisstein's World of Mathematics, Squircle

Crossrefs

Cf. A175576 for decimal expansion.

Programs

Maple

convert(8*GAMMA(5/4)^2/sqrt(Pi), confrac, 84); # Peter Luschny, Sep 02 2021

Mathematica

ContinuedFraction[Pi^(3/2)/Gamma[3/4]^2, 84] (* Michael De Vlieger, Sep 01 2021 *)

PARI

contfrac(Pi^1.5/gamma(3/4)^2) \\ Michel Marcus, Sep 02 2021

Formula

Equals sqrt(2)*Pi/agm(1,sqrt(2)) (arithmetic-geometric mean).

Equals 8*Gamma(5/4)^2/sqrt(Pi). - Peter Luschny, Sep 02 2021