The first Debye function is defined by
(1)
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(2)
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for , , and are Bernoulli numbers. Particular values are given by
(3)
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(4)
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(5)
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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)
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(7)
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for and .
The sum of these two integrals is
(8)
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(9)
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where is the Riemann zeta function.