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