  In this paper, we introduce degenertae generalized hypergeometric functions
and study degenerate hypergeometric numbers of order p. These numbers involving
of lambda-binomial coefficients and lambda-falling sequence, and can be
represented by means of the degenerate generalized hypergeometric functions. we
will derive some explicit expressions and combinatorial identities for those
numbers. We also consider several related special numbers like
lambda-hypergeometric numbers of order p and Apostol type lambda-hypergeometric
numbers of order p, of which the latter reduce in a limiting case to the
generalized p-th order Franel numbers.
