OFFSET
0,1
LINKS
Muthu Veerappan Ramalingam, An Expected Value Problem
FORMULA
Equals (2 - 2 * sqrt(2)) / (3 * Pi) + (2 / Pi) * cosech^{-1}(1)
Equals (a^3 + b^3 - d^3) / (3 * Pi * a * b) + (a / Pi) * cosech^{-1}(a / b) + (b / Pi) * cosech^{-1}(b / a) for an arbitrary rectangle with sides a, b and diagonal d.
EXAMPLE
0.47320100440933855164249820976301198129996056896363...
MATHEMATICA
N[(2 - 2 Sqrt[2])/3/Pi + 2 ArcCsch[1]/Pi, 50]
PROG
(PARI) arcsch(x) = log(1/x + sqrt(1+1/x^2));
(2 - 2*sqrt(2))/(3*Pi) + (2/ Pi)*arcsch(1) \\ Michel Marcus, Jan 16 2020
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Muthu Veerappan Ramalingam, Jan 03 2020
STATUS
approved