  We present analytic properties and extensions of the constants ck appearing
in the Baez-Duarte criterion for the Riemann hypothesis. These constants are
the coefficients of Pochhammer polynomials in a series representation of the
reciprocal of the Riemann zeta function. We present generalizations of this
representation to the Hurwitz zeta and many other special functions. We relate
the corresponding coefficients to other known constants including the Stieltjes
constants and present summatory relations. In addition, we generalize the
Maslanka hypergeometric-like representation for the zeta function in several
ways.
