Persymmetric determinants

The object of this paper is to develop some of the results in the author's joint paper with Dale 2] concerning the derivatives of persymmetric determinants whose elements are Appell functions.Four new double-sum identities are presented which are valid for arbitrary persymmetric determinants. Two of these identities are applied to give direct proofs of two results in 2], A simple formula is given for the derivative of a Turanian of order n with Appell polynomial elements and the result is applied repeatedly to show that its degree is far lower than expected. It is shown that one particular determinant has simple derivatives of all orders and that its degree too is far lower than expected. The formula for the derivative of (first) cofactors is shown to be extensible in a simple manner to the derivatives of second cofactors.