  Form factors in the sinh-Gordon model are studied semiclassically for small
values of the parameter $b\sim\hbar^{1/2}$ in the background of a radial
classical solution, which describes a heavy exponential operator placed at the
origin. For this purpose we use a generalization of the radial quantization
scheme, well known for a massless boson field. We introduce and study new
special functions which generalize the Bessel functions and have a nice
interpretation in the Tracy-Widom theory of the Fredholm determinant solutions
of the classical sinh-Gordon model. Form factors of the exponential operators
in the leading order are completely determined by the classical solutions,
while form factors of the descendant operators contain quantum corrections even
in this approximation. The construction of descendant operators in two
chiralities requires renormalizations similar to those encountered in the
conformal perturbation theory.
