  We present some classical and weighted Poincar\'e inequalities for some
one-dimensional probability measures. This work is the one-dimensional
counterpart of a recent study achieved by the authors for a class of
spherically symmetric probability measures in dimension larger than 2. Our
strategy is based on two main ingredients: on the one hand, the optimal
constant in the desired weighted Poincar\'e inequality has to be rewritten as
the spectral gap of a convenient Markovian diffusion operator, and on the other
hand we use a recent result given by the two first authors, which allows to
estimate precisely this spectral gap. In particular we are able to capture its
exact value for some examples.
