Integrals over the Fermi–Dirac and Bose–Einstein distributions define a “poly” form of this function. (10[1])The replica trick takes advantage (10[1])of the fact that this function (10[1])of Z (10[1])is equal to the limit as n (10[1])approaches zero of “Z-to-the-n, (-5[1])minus one, all over n.” The expected value of the energy (-5[1])is equal to the negative partial derivative (10[1])of this function of Z with respect to beta. (-5[1])The Helmholtz (10[1])free energy (10[1])is equal to kT times this function (-5[1])of the partition (10[1])function. (10[1])Stirling’s formula (10[1])approximates (-5[2])this function (-5[5])of (-5[1])n-factorial. (10[3]-5[5])The negative (10[1])sum over all states of “p times this function of p” defines the Shannon entropy, while Boltzmann’s definition of entropy is equal (10[1])to k times (10[1])this function (-5[1])of the number of microstates. For 10 points, name this function, (10[1])the inverse of the exponential function. (10[4])■END■ (10[19]0[1])