On functionals of excursions for Bessel processes with negative index

A closed formula is given for the integral of functionals on the space of excursions from a point z >= 0 of a Bessel process R-(mu) with index mu is an element of (-1, 0) with respect to the characteristic (Ito) measure. This integral is an integral with respect to some kernel K. The kernel K is found due to the explicit form of the joint distribution of (tau(z), R-t((mu))) at fixed time t and for tau(z) being the first hitting time of the point z by the process R-(mu). The expected time spent by an excursion in an interval with respect to the Ito measure is calculated.