A family of gauss-kronrod quadrature formulae

We show, for each n ≥ 1, that the (2n + l)-point Kronrod extension of the n-point Gaussian quadrature formula for the measure dσr(t) = (1 + r)2(1 - t2)1/2dt/((l + r))2 – 4rt2)-1 <r≤ 1, has the properties that its n + 1 Kronrod nodes interlace with the n Gauss nodes and all its 2n+ 1 weights are positive. We also produce explicit formulae for the weights. © 1988 American Mathematical Society.