A closed-form expression for the Sharma-Mittal entropy of exponential   families
  The Sharma-Mittal entropies generalize the celebrated Shannon, R\'enyi and Tsallis entropies. We report a closed-form formula for the Sharma-Mittal entropies and relative entropies for arbitrary exponential family distributions. We instantiate explicitly the formula for the case of the multivariate Gaussian distributions and discuss on its estimation. 
Frank Nielsen and Richard Nock
cs.IT math.IT