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A347430 Simple continued fraction expansion of Pi^(3/2)/Gamma(3/4)^2. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..83.

M. Parker, What is the area of a Squircle?, Youtube video (2021).

Eric Weisstein's World of Mathematics, Squircle

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

EXAMPLE

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

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 *)

PROG

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

CROSSREFS

Cf. A175576 for decimal expansion.

Sequence in context: A139381 A225849 A038575 * A346491 A304302 A305516

Adjacent sequences:  A347427 A347428 A347429 * A347431 A347432 A347433

KEYWORD

nonn,cofr

AUTHOR

Adam Filinovich, Sep 01 2021

STATUS

approved

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Last modified January 22 07:31 EST 2022. Contains 350481 sequences. (Running on oeis4.)