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

Authors:
Grzegorz Rząkowski;SBawomir Łepkowski
Affiliations:
Faculty of Mathematics and Natural Sciences, Cardinal Stefan Wyszyński University in Warsaw, Warsaw, Poland 01-815;Faculty of Mathematics and Natural Sciences, Cardinal Stefan Wyszyński University in Warsaw, Warsaw, Poland 01-815
Venue:
Journal of Scientific Computing
Year:
2008

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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.