The Collaborative International Dictionary of English v.0.48:

Convergence \Con*ver"gence\, Convergency \Con*ver"gen*cy\, n.
   [Cf. F. convergence.]
   1. The condition or quality of converging; tendency to one
      point; the occurrence of two or more things coming
      together.
      [1913 Webster]

   2. (Math.) the approach of an infinite series to a finite
      limit.

   Syn: convergency.
        [WordNet 1.5]

   3. a representation of common ground between theories or
      phenomena.

   Syn: overlap, intersection.
        [WordNet 1.5]

   4. the act of converging (coming closer).

   Syn: converging, convergency.
        [WordNet 1.5]

   5. (Biol.) a similarity of form or function in two or more
      organisms caused by evolutionary adaptations to a
      similarity in the environment, rather than to a common
      heredity.
      [PJC]

            The convergence or divergence of the rays falling on
            the pupil.                            --Berkeley.
      [1913 Webster]

WordNet (r) 3.0 (2006):

convergency
    n 1: the approach of an infinite series to a finite limit [syn:
         convergence, convergency] [ant: divergence,
         divergency]
    2: the act of converging (coming closer) [syn: convergence,
       converging, convergency]