Recurrence relations of orthogonal polynomials in H01 and H02

Takehiko Kinoshita, Yoshitaka Watanabe, Mitsuhiro T. Nakao
2015 Nonlinear Theory and Its Applications IEICE  
We present a three term recurrence relation of orthogonal polynomials for H 1 0 and H 2 0 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 H 1 0 and H 2 0 were not known up to now. In this paper, the three term
more » ... 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.
doi:10.1587/nolta.6.404 fatcat:etyxcfztxnd67nz533wzwmnfc4