Entropic uncertainty relation for power-law wave packets

For the power-law quantum wave packet in configuration space, the variance of the position observable may be divergent, and, accordingly, the Heisenberg-type formulation of the uncertainty principle becomes weak. In contrast to such a situation, the information-entropic formulation involves only finite quantities, thus displaying its superiority over the Heisenberg-type relation. We attempt to clarify here just how the total amount of entropic uncertainty converges to its lower bound in the limit of a large value for the exponent of the power-law wave packet.