  We consider quadrature formulas based on interpolation using the basis
functions $1/(1+t_kx)$ $(k=1,2,3,\ldots)$ on $[-1,1]$, where $t_k$ are
parameters on the interval $(-1,1)$. We investigate two types of quadratures:
quadrature formulas of maximum accuracy which correctly integrate as many basis
functions as possible (Gaussian quadrature), and quadrature formulas whose
nodes are the zeros of the orthogonal functions obtained by orthogonalizing the
system of basis functions (orthogonal quadrature). We show that both approaches
involve orthogonal polynomials with modified (or varying) weights which depend
on the number of quadrature nodes. The asymptotic distribution of the nodes is
obtained as well as various interlacing properties and monotonicity results for
the nodes.
