|
|
A175576
|
|
Decimal expansion Pi^(3/2)/Gamma(3/4)^2.
|
|
6
|
|
|
3, 7, 0, 8, 1, 4, 9, 3, 5, 4, 6, 0, 2, 7, 4, 3, 8, 3, 6, 8, 6, 7, 7, 0, 0, 6, 9, 4, 3, 9, 0, 5, 2, 0, 0, 9, 2, 4, 3, 5, 1, 9, 7, 6, 4, 7, 0, 4, 3, 5, 3, 3, 8, 1, 1, 1, 7, 1, 8, 5, 6, 0, 9, 0, 1, 1, 2, 0, 4, 3, 5, 5, 3, 6, 7, 6, 2, 3, 9, 9, 5, 6, 7, 1, 4, 5, 4, 3, 7, 2, 3, 3, 0, 0, 7, 4, 3, 7, 9, 4, 5, 5, 5, 5, 4
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Entry 34 e of chapter 11 of Ramanujan's second notebook.
In addition, Pi^(3/2) / Gamma(3/4)^2 is the area of the unit "squircle" as defined in MathWorld. (Note that 8*Gamma(5/4)^2 / sqrt(Pi) is the same constant.) - Jean-François Alcover, Feb 24 2011
Also equals Integral_{-infinity, infinity} 1/(1+2*x^2)^(3/4) or Integral_{-infinity, infinity} 1/sqrt(1+x^4). - Jean-François Alcover, Jun 04 2013
|
|
LINKS
|
Eric Weisstein's World of Mathematics, Squircle
|
|
FORMULA
|
Equals 3*Sum_{n >= 0} (1/(4*n+1) + 1/(4*n-3))*binomial(1/2,n). Cf. A290570.
Equals hypergeom([-1/2, 3/4, -3/4], [-1/4, 5/4], -1).
Equals 2*hypergeom([1/4, 3/4], [5/4], 1) = (16/5)*hypergeom([-1/4, -3/4], [5/4], 1). (End)
|
|
EXAMPLE
|
3.708149354602743836867700...
|
|
MAPLE
|
Pi^(3/2)/GAMMA(3/4)^2 ; evalf(%) ;
|
|
MATHEMATICA
|
RealDigits[Pi*EllipticTheta[3, 0, Exp[-Pi]]^2, 10, 50][[1]]
RealDigits[Pi^(3/2)/(Gamma[3/4])^2, 10, 50][[1]] (* G. C. Greubel, Feb 12 2017 *)
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|