It is known that the radial equation of the massless fields with spin around
Kerr black holes cannot be solved by special functions. Recently, the analytic
solution was obtained by use of the expansion in terms of the special functions
and various astrophysical application have been discussed. It was pointed out
that the coefficients of the expansion by the confluent hypergeometric
functions are identical to those of the expansion by the hypergeometric
functions. We explain the reason of this fact by using the integral equations
of the radial equation. It is shown that the kernel of the equation can be
written by the product of confluent hypergeometric functions. The integral
equaton transforms the expansion in terms of the confluent hypergeometric
functions to that of the hypergeometric functions and vice versa,which explains
the reason why the expansion coefficients are universal.Comment: 14 pages, LaTeX, no figure