Debye Functions
The first Debye function is defined by
for 
, 
, and 
are Bernoulli numbers. Particular values are given by
where 
is a polylogarithm and 
is the Riemann zeta function. Abramowitz and Stegun (1972, p. 998) tabulate numerical values of 
for 
to 4 and 
to 10.
The second Debye function is defined by
for 
and 
.
The sum of these two integrals is
where 
is the Riemann zeta function.
REFERENCES:
Abramowitz, M. and Stegun, I. A. (Eds.). "Debye Functions." §27.1 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 998, 1972.
Beattie, J. A. "Six-Place Tables of the Debye Energy and Specific Heat Functions." J. Math. Phys. 6, 1-32, 1926.
Grüneisen, E. "Die Abhängigkeit des elektrischen Widerstandes reiner Metalle von der Temperatur." Ann. Phys. 16, 530-540, 1933.
