A GAUSSIAN QUADRATURE FOR THE CALCULATION OF GENERALIZED FERMI-DIRAC INTEGRALS

In a recent paper, Pichon has addressed the problem of computing generalized Fermi-Dirac integrals with the use of a Gauss-Laguerre type quadrature. As an alternative solution, we investigate Gaussian quadrature based on weight functions of the form x(k)/(e(x) + 1), for k = 1/2, 3/2, 5/2, and show that the required number of functional evaluations for a desired accuracy is superior in some instances to the properly parametrized Gauss-Laguerre rule. Moreover, the method presented here is independent of parameter adjustment as opposed to the case of the Gauss-Laguerre.