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

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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.

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Authors and Affiliations

  1. Faculty of Mathematics and Natural Sciences, Cardinal Stefan Wyszyński University in Warsaw, Dewajtis 5, 01-815, Warsaw, Poland

    Grzegorz Rza̧dkowski & Sławomir Łepkowski

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  1. Grzegorz Rza̧dkowski
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  2. Sławomir Łepkowski
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Correspondence to Grzegorz Rza̧dkowski.

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Rza̧dkowski, G., Łepkowski, S. A Generalization of the Euler-Maclaurin Summation Formula: An Application to Numerical Computation of the Fermi-Dirac Integrals. J Sci Comput 35, 63–74 (2008). https://doi.org/10.1007/s10915-007-9175-3

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  • DOI: https://doi.org/10.1007/s10915-007-9175-3

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