Generalized quadrature formulae for analytic functions

A kind of generalized quadrature formulae of maximal degree of precision for numerical integration of analytic functions is considered. Precisely, a general weighted quadrature of Birkhoff–Young type with 4n+34n+3 nodes and degree of precision 6n+56n+5 is studied. Its nodes are characterized by an orthogonality relation and a general numerical method for their computation is given. Special cases and numerical results are also included.