Some properties of the integrals of even and odd parts of Hurwitz polynomials

Given the zeros of the even or the odd parts of Hurwitz polynomials (HP), conditions have been established such that their integrals are suitable as the odd or the even parts of other HP's. Testing procedures, including simple inspection tests, have been enunciated for both cases. The criteria developed can be used to generate positive real functions (prf) of higher order.