  Miller-Paris transformations are extensions of Euler's transformations for
the Gauss hypergeometric functions to generalized hypergeometric functions of
higher-order having integral parameter differences (IPD). In our recent work we
computed the degenerate versions of these transformations corresponding to the
case when one parameter difference is equal to a negative integer. The purpose
of this paper is to present an independent new derivation of both the general
and the degenerate forms of Miller-Paris transformations. In doing so we employ
the generalized Stieltjes transform representation of the generalized
hypergeometric functions and some partial fraction expansions. Our approach
leads to different forms of the characteristic polynomials, one of them appears
noticeably simpler than the original form due to Miller and Paris. We further
present two extensions of the degenerate transformations to the generalized
hypergeometric functions with additional free parameters and additional
parameters with negative integral differences.
