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We have labeled this integral by the subscript "eq" (standing for "equilibrium") to
emphasize explicitly the fact that it is to be evaluated for any process by which the
system is brought quasi- statically through a sequence of near-equilibrium ...
Then dx = •^a_,M~1 du, and the integral assumes the form 7(n) = J0" e— du By
virtue of the definition (A -3 -4) of the r function, this can then be written ^ /(») B Jo
" e— x» = ^ T (^-^) «-(s+1)/2 (A-4-5) Using the property (A- 3 -6) of the T function ...
The sum (A- 11-2) suggests a sum of residues at all integral values. Since the
function (tan rz)_1 has simple poles at all integral values, it follows that the sum (
A- 11 -2) can be expressed in terms of a contour integral along the path C of Fig.
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Reif: fundamental of statistical thermal physics
Introduction to statistical methods
GENERAL DISCUSSION OF THE RANDOM WALK
Statistical description of systems of particles
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