Table of the zeros and weight factors of the first fifteen Laguerre polynomials

The chief use of the present table of zeros and weight factors of the Laguerre polynomials is in the performance of quadratures over the interval [0, oo ], when the integrand behaves like the product of e~~ by a polynomial. From the well known theory of orthogonal polynomials, the quadrature formula is exact for any polynomial P(x) up to the (In — l ) th degree, provided one uses the w-point quadrature formula. Thus if a* denotes the "weight factors" or "Christoffel numbers," corresponding to Ln(x), the nth Laguerre polynomial, and xl denotes the zeros of Ln(x), then