  The transmutation (transformation) operator associated with the perturbed
Bessel equation is considered. It is shown that its integral kernel can be
uniformly approximated by linear combinations of constructed here generalized
wave polynomials, solutions of a singular hyperbolic partial differential
equation arising in relation with the transmutation kernel. As a corollary of
this results an approximation of the regular solution of the perturbed Bessel
equation is proposed with corresponding estimates independent of the spectral
parameter.
