 TOPICS # 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.

Polylogarithm

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## 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.

Debye Functions

## Cite this as:

Weisstein, Eric W. "Debye Functions." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DebyeFunctions.html