What is the general term of (x-a) (x-b) (x-c) …(x-n) where n is a positive no and a,b, c,…n are in AP? I have a function [math]f:\mathbf{R}^n \to \mathbf{R}^{m}[/math] for m>n.  How can I define a function [math]B:\mathbf{R}^n \to \mathbf{R}^{n \times m}[/math] such that [math]\forall_{X \in \mathbf{R}^n} [/math] the columns of B(X) form a basis for the n-hyperplane whose normal vector is parallel to f(X)?