Abstract
We survey some polynomials {P-n} arising from convergence acceleration, and numerical integration, that satisfy "biorthogonality" conditions such as integral(b)(a) P-n (x) phi(j) (x) w (x) dx = 0, for appropriate functions {phi(j)} and weights w. One example is phi(j) (x) = (log x)(j) , 0 <= j <= n - 1 on [a, b] = [0, 1]. We discuss identities, asymptotics, positive quadratures, and zero distributions. We also list some open questions. (c) 2021 Elsevier B.V. All rights reserved.
NSTL
Elsevier