  Important new transformations for the generalized hypergeometric functions
with integral parameter differences have been discovered some years ago by
Miller and Paris and studied in detail in a series of papers by a number of
authors. These transformations fail if the free bottom parameter is greater
than a free top parameter by a small positive integer. In this paper we fill
this gap in the theory of Miller-Paris transformations by computing the limit
cases of these transformations in such previously prohibited situations. This
leads to a number of new transformation and summation formulas including
extensions of Karlsson-Minton theorem.
