  We introduce the power collection method for easily deriving connection
relations for certain hypergeometric orthogonal polynomials in the $(q-)$Askey
scheme. We summarize the full-extent to which the power collection method may
be used. As an example, we use the power collection method to derive connection
and connection-type relations for Meixner and Krawtchouk polynomials. These
relations are then used to derive generalizations of generating functions for
these orthogonal polynomials. The coefficients of these generalized generating
functions are in general, given in term of multiple hypergeometric functions.
From derived generalized generating functions, we derive corresponding contour
integral and infinite series expressions by using orthogonality.
