Recurrence relations of orthogonal polynomials in H01 and H02

We present a three term recurrence relation of orthogonal polynomials for H01 and H02 spaces. If there were explicit formulas for such orthogonal polynomials, they would be very convenient for various kinds of practical computations. As long as such formulas are not available recurrence relations may effictively substitute them. As far as the authors know, these recurrence relations of orthogonal polynomials for H01 and H02 were not known up to now. In this paper, the three term recurrence relations of these orthogonal polynomials were derived by using properties of Legendre polynomials. Our results will enable us to simplify computational procedures in the spectral approximation methods.