caa a22 4500 475777018 CHVBK 20180406123633.0 cr unu---uuuuu 170329e20001201xx s 000 0 eng 10.1023/A:1011136831736 doi (NATIONALLICENCE)springer-10.1023/A:1011136831736 Lether Frank E-mail: fglether@math.uga.edu aut Analytical Expansion and Numerical Approximation of the Fermi-Dirac Integrals $$F$$ j (x) of Order j=−1/2 and j=1/2 [Elektronische Daten] [Frank Lether] This paper uses properties of the Weyl semiintegral and semiderivative, along with Oldham's representation of the Randles-Sevcik function from electrochemistry, to derive infinite series expansions for the Fermi-Dirac integrals $$F$$ j (x), −∞<x<∞, j=−1/2, 1/2. The practical use of these expansions for the numerical approximation of $$F$$ −1/2(x) and $$F$$ 1/2(x) over finite intervals is investigated and an extension of these results to the higher order cases j=3/2, 5/2, 7/2 is outlined. Plenum Publishing Corporation, 2000 Fermi-Dirac integral nationallicence Randles-Sevcik function nationallicence semiintegral nationallicence semiderivative nationallicence electrochemistry nationallicence Journal of Scientific Computing Kluwer Academic Publishers-Plenum Publishers 15/4(2000-12-01), 479-497 0885-7474 15:4<479 2000 15 10915 https://doi.org/10.1023/A:1011136831736 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1011136831736 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Lether Frank E-mail: fglether@math.uga.edu aut NATIONALLICENCE 773 0- Journal of Scientific Computing Kluwer Academic Publishers-Plenum Publishers 15/4(2000-12-01), 479-497 0885-7474 15:4<479 2000 15 10915 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer