  Indefinite inner product spaces of entire functions and functions analytic
inside a disk are considered and their completeness studied. Spaces induced by
the rotation invariant reproducing kernels in the form of the generalized
hypergeometric function are completely characterized. A particular space
generated by the modified Bessel function kernel is utilized to derive an
analytic continuation formula for functions on $R^+$ using the best
approximation theorem of S. Saitoh. As a by-product several new area integrals
involving Bessel functions are explicitly evaluated
