Vertices of Plane Curves

PROOF. Apply Theorem J for the case w==r. We obtain for gr an expression which differs from the one just written only in the fact that the terms Brtr+ifr+i+Brtr+2fr+2+ • • • +Br,nfn are missing from its numerator. But the coefficients J3r,, = 0 when r<s. Hence the two expressions are equal. REMARK. The generalization of the method to orthonormalization with respect to a general norming or weight function p is obvious. One applies the process described to the functions (p)fi and obtains functions g% (=linear combinations of the (p)fi) which are orthonormal with respect to the weight function unity. Dividing through by the common factor (p) one forms functions gi(p)~~* which are orthonormal with respect to p.