  In the paper we find solution representations in the compact integral form to
the Cauchy problem for a general form of the Euler--Poisson--Darboux equation
with Bessel operators via generalized translation and spherical mean operators
for all values of the parameter $k$, including also not studying before
exceptional odd negative values. We use a Hankel transform method to prove
results in a unified way. Under additional conditions we prove that a
distributional solution is a classical one too. A transmutation property for
connected generalized spherical mean is proved and importance of applying
transmutation methods for differential equations with Bessel operators is
emphasized. The paper also contains a short historical introduction on
differential equations with Bessel operators and a rather detailed reference
list of monographs and papers on mathematical theory and applications of this
class of differential equations.
