On the Theory of Biorthogonal Polynomials

Let <!-- MATH $\varphi (x,\,\mu )$ --> be a distribution in <!-- MATH $x \in {\mathbf{R}}$ --> for every in a real parameter set . Subject to additional technical conditions, we study th degree monic polynomials that satisfy the biorthogonality conditions <!-- MATH \begin{displaymath} \int_{ - \infty }^\infty {{p_m}(x)\,d\varphi (x,{\mu _l}) = 0,} \qquad l = 1,\,2, \ldots ,\,m,\;m \geqslant 1 \end{displaymath} -->