We present a new approach to the design of D-optimal experiments with multivariate polynomial regressions on compact semi-algebraic design spaces. We apply the moment-sum-of-squares hierarchy of semidefinite programming problems to solve numerically and approximately the optimal design problem. The geometry of the design is recovered with semidefinite programming duality theory and the Christof...

A generalized connection, including Christoffel coefficients, torsion, non-metricity tensor and metric-asymmetricity object, is analyzed according to the Schouten classification. The inverse structure matrix is found in the linearized regime, autoparallel trajectories are defined and the contribution of the components of the connection are clarified at first-order approximation.

We give a remarkable additional othogonality property of the classical Legendre polynomials on the real interval [−1, 1]: polynomials up to degree n from this family are mutually orthogonal under the arcsine measure weighted by the degree-n normalized Christoffel function.

We derive analogues for Bessel functions of what is known as the Christoffel-Darboux identity for orthonormal polynomials: ∞ ∑ k=1 2 (ν + k) Jν+k(w) Jν+k(z) = wz w − z ( Jν+1(w) Jν(z)− Jν(w) Jν+1(z) )

Let {λj}j=1 be a sequence of distinct positive numbers. We find explicit formulae for the orthogonal Dirichlet polynomials {ψn} formed from linear combinations of { λ−it j }n j=1 , associated with the Laguerre weight. Thus ∫ ∞ 0 ψn (t)ψm (t)e −tdt = δmn. In addition, we estimate Christoffel functions and establish Markov-Bernstein inequalities.