  Using a lemma of Davis on Gram matrices applied to the classical Orthogonal
Polynomials to generate reproducing kernel interpolation over the classical
domains for polynomials. These kernels have terms which are exact over the
rational ring. The Condition Numbers are readily shown to get very large with
the size of the Gram matrices as expected. The calculation of the error
variances for trigonometric functions and the exponential show a significant
improvement over the equivalent Taylor expansion variances.
