Abstract
We obtain a fast convergent series expansion for the Fermi–Dirac function Fs(a) for −10<a⩽1. We give values of Fs(a) for s = n+ 1/2 (n = 0,1,⋅⋅⋅,6) with a in the same range.
Highlights
The Fermi-Dirac functions F(7 (a), where £7 is a positive real parameter, is defined for all real numbers a by a1Jo + Fa(a) = T(£17) "" eXx+u- 1 dx.When £7 is an integer, this integral may be evaluated by a power series; a complete discussion of this case is due to Rhodes
I For arbitrary a, there are several expansions depending on the range of values of a. 2--4 The calculation of F,(a) for a < 0 is needed in many questions of quantum statistical mechanics; for example, to solve the equations of state corresponding to extreme conditions
Analytical expansions are available in all ranges, except when - lO
Summary
The Fermi-Dirac functions F(7 (a), where £7 is a positive real parameter, is defined for all real numbers a by a1. Previous evaluations of Fa(a) for this range were made by numerical integration4.5 or by polynomial approximation.. In this paper we obtain a fast convergent series expansion of Fa(a) for - lO
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
