Let A be an n × n complex matrix and 0 ≤ q ≤ 1. The boundary of the q-numerical range of A is the orthogonal projection of a hypersurface defined by the dual surface of the homogeneous polynomial F (t, x, y, z) = det(t In + x(A + A )/2 + y(A−A)/(2i) + z AA). We construct different types of cubic surfaces SF corresponding to the homogeneous polynomial F (t, x, y, z) induced by some 3 × 3 matrice...

In order to find a general framework for different combinatorial identities and identities that involve special functions, Bernshtein introduced in [1] a notion of holonomic functions. Let us recall this definition (in formulating it, we will follow [10]). A discrete holonomic function f(n) of one variable is defined as a solution of a homogeneous, linear difference equation with polynomial coe...