A Generalization of the Euler-Maclaurin Summation Formula: An Application to Numerical Computation of the Fermi-Dirac Integrals

Abstract The present paper deals with a generalization of the Euler-Maclaurin summation formula. The generalization is based on Bernoulli functions which are expressed in an integral form involving Bernoulli polynomials. Then the formula is used to numerical computation of the Fermi-Dirac integrals.