Orthogonal Polynomials

abscissas according analytic function arbitrary and real argument assume asymptotic formula Chapter coefficients complex const constant factor continuous function convergence corresponding decreasing defined denote derived differential equation establishes the statement exists expansion expression Fejér finite fixed positive number following theorem function f(x furnishes Hermite polynomials holds uniformly Ibid inequality integral interior interval Jacobi polynomials Lagrange Lagrange polynomials Laguerre polynomials Legendre polynomials Let f(x log f(0 Mathematische maximum method nomials non-negative notation obtain orthogonal polynomials P(cos Pn(x poly polynomial p(x precise problem proof of Theorem properties replaced representation respectively result right-hand member satisfies the conditions segment sequence similar sin² solution step polynomials Stieltjes Szegö Tchebichef term trigonometric polynomial unit circle upper bound values vanishes weight function write x₁ zeros