Symbolic-numeric computation of orthogonal polynomials and Gaussian quadratures with respect to the cardinal B-spline.

The first 60 coefficients in the three-term recurrence relation for monic polynomials orthogonal with respect to cardinal B-splines φ as the weight functions on [0, m] ( m ∈ ℕ) are obtained in a symbolic form. They enable calculation of parameters, nodes, and weights, in the corresponding Gaussian quadrature up to 60 nodes. The efficiency of these Gaussian quadratures is shown in some numerical examples. Finally, two interesting conjectures are stated. [ABSTRACT FROM AUTHOR]