OFFSET
0,1
FORMULA
Equals (a/b - b/a)*b^(1/2), where a = sqrt(2)*Gamma(5/4)^2 and b = Pi/4.
Equals sqrt(2) * (EllipticK(sqrt(2)/2) - EllipticE(sqrt(2)/2)).
Equals Integral_{x=0..Pi/2} cos(x)^2 / sqrt(1 + sin(x)^2).
EXAMPLE
0.7119586597782638015124585488053977677277711441...
MAPLE
Digits := 100: a := sqrt(2)*GAMMA(5/4)^2: b := Pi/4: evalf((a/b - b/a)*b^(1/2), Digits)*10^90: ListTools:-Reverse(convert(floor(%), base, 10));
MATHEMATICA
With[{a = Sqrt[2]*Gamma[5/4]^2, b = Pi/4}, RealDigits[(a/b - b/a)*b^(1/2), 10, 120][[1]]] (* Amiram Eldar, Nov 19 2022 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Peter Luschny, Nov 19 2022
STATUS
approved