-------- Basic homogeneity property: >>> import numpy as np >>> from scipy.special import elliprd >>> x = 1.2 + 3.4j >>> y = 5. >>> z = 6. >>> scale = 0.3 + 0.4j >>> elliprd(scale*x, scale*y, scale*z) (-0.03703043835680379-0.24500934665683802j) >>> elliprd(x, y, z)*np.power(scale, -1.5) (-0.0370304383568038-0.24500934665683805j) All three arguments coincide: >>> x = 1.2 + 3.4j >>> elliprd(x, x, x) (-0.03986825876151896-0.14051741840449586j) >>> np.power(x, -1.5) (-0.03986825876151894-0.14051741840449583j) The so-called "second lemniscate constant": >>> elliprd(0, 2, 1)/3 0.5990701173677961 >>> from scipy.special import gamma >>> gamma(0.75)**2/np.sqrt(2*np.pi) 0.5990701173677959 Ú