I just taught maxima what the value of elliptic_ec(-1) is:
elliptic_ec(-1);
sqrt(2)*elliptic_ec(1/2)
However, maxima also knows that elliptic_ec(1/2) is
gamma(3/4)^2/(2*sqrt(%pi))+%pi^(3/2)/(4*gamma(3/4)^2)
Should elliptic_ec(-1) evaluate to
gamma(3/4)^2/(sqrt(2)*sqrt(%pi))+%pi^(3/2)/(2^(3/2)*gamma(3/4)^2)
instead of sqrt(2)*elliptic_ec(1/2)?
Ray