  Generalizing the construction of the cyclotomic Gaudin algebra from
arXiv:1409.6937, we define the universal cyclotomic Gaudin algebra. It is a
cyclotomic generalization of the Gaudin models with irregular singularities
defined in arXiv:math/0612798.
  We go on to solve, by Bethe ansatz, the special case in which the Lax matrix
has simple poles at the origin and arbitrarily many finite points, and a double
pole at infinity.
