On Some Problems of P. Turán Concerning Lm Extremal Polynomials and Quadrature Formulas Original Research Article

The Lm extremal polynomials in an explicit form with respect to the weights (1−x)−1/2 (1+x)(m−1)/2 and (1−x)(m−1)/2 (1+x)−1/2 for even m are given. Also, an explicit representation for the Cotes numbers of the corresponding Turán quadrature formulas and their asymptotic behavior is provided.