  We prove that the native space of a Wu function is a dense subspace of a
Sobolev space. An explicit characterization of the native spaces of Wu
functions is given. Three definitions of Wu functions are introduced and proven
to be equivalent. Based on these new equivalent definitions and the so called
$f$-form tricks, we can generalize the Wu functions into the even-dimensional
spaces $\R^{2k}$, while the original Wu functions are only defined in the
odd-dimensional spaces $\R^{2k+1}$. Such functions in even-dimensional spaces
are referred to as the `missing Wu functions'. Furthermore we can generalize
the Wu functions into `fractional'-dimensional spaces. We call all these Wu
functions the generalized Wu functions. The closed form of the generalized Wu
functions are given in terms of hypergeometric functions. Finally we prove that
the Wu functions and the missing Wu functions can be written as linear
combinations of the generalized Wendland functions.
