Some biorthogonal polynomials arising in numerical analysis and approximation theory

We survey some polynomials Pn arising from convergence acceleration, and numerical integration, that satisfy ”biorthogonality” conditions such as ∫abPnxϕjxwxdx=0,for appropriate functions ϕj and weights w. One example is ϕjx=logxj,0≤j≤n−1 on a,b=0,1. We discuss identities, asymptotics, positive quadratures, and zero distributions. We also list some open questions.