Debye Functions

The first Debye function is defined by

			(1)
			(2)

for , , and  are Bernoulli numbers. Particular values are given by

			(3)
			(4)
			(5)

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

			(6)
			(7)

for  and .

The sum of these two integrals is

			(8)
			(9)

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.