I keep in memory (qos(x))^4+(qin(x))^4=1 and : qin(sigma/2)=1, qin(sigma/4)=2^(-1/4) . I looked for the equivalent of the formula Gamma(1-z)*Gamma(z)=Pi/(sin(z*Pi)) with the function qin(x). I imagined that the following equalities are correct, I could verify numerically. integrate((1-x^4)^(-3/4), x, 0, 1)=(sigma/2)/qin(sigma/2); integrate(x^4*(1-x^8)^(-7/8), x, 0, 1)=(sigma/4)/qin(sigma/4); but I was wrong about this equality, it is not correct. integrate(x^12*(1-x^16)^(-15/16), x, 0, 1) = (sigma/8)/qin(sigma/8); Why ??? The first answer may be related to the nature of the squircle itself, on an axis, its area can not be divided into several equal parts. We can only get 2 or 4 equal parts. but I remain convinced that there must be this type of formula