Abstract
After a brief indication of the types of physical problem in which they arise, an account is given of methods of evaluation of the Fermi-Dirac functions,
F
n
(
ƞ
) = ∫
0
∞
{
x
n
/e
z-ƞ
+ 1)}
dx
, for positive integral values of
n
. The following relationship is derived:
F
n
( + |
ƞ
|) + (-)
n+1
F
n
(- |
ƞ
|) =
S
n
( + |
ƞ
|), where
S
n
(
ƞ
) = (
ƞ
n+1
)/(n+1) {1 + ∑ 2(n + 1)n...(n - 2r + 2) (1 - 2
1-2r
) ζ(2r)
ƞ
-2r
}; and the expressions for
S
n
(
ƞ
) are tabulated for n = 1,2, 3, 4. A series suitable for the evaluation of
F
n
( - |
ƞ
|) to any required accuracy is indicated; together with the derived relationship this provides a means by which
F
n
( + |
ƞ
|) may be computed to any required accuracy. To facilitate the use of the functions the values of (1/n!)
F
n
( - |
ƞ
|) for n = 1, 2, 3, 4 have been calculated and are tabulated to seven decimal places for
ƞ
= 0.0(0.1) 4.0.
Reference18 articles.
1. Davis H. T. (ed.) 1933 Tables of the higher mathematical functions 1. Bloomington In d .: Prineipia Press.
2. Dwight H. B. 1945 Tables of integrals and other mathematical data. New York: Macmillan.
3. Lowan A. N. etal 1939 Tables of the exponential function. New York: Work Projects Administration.
4. Lowan A. N. etal 1941 Table of natural logarithms 3 4. New York: Work Projects Administration.
5. The computation of Fermi-Dirac functions
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