Polynomial approximation of neutron flux in the method of first collision probabilities

Neutron flux in each zone is supposed to be constant in the method of first collision probabilities. Presupposed is generalization of neutron flux approximation in each zone by polynomial from Cartesian coordinates. Prosented is a calculation method of generalized probabilities of first collisions. It is proved, that in this case the integral multiplicity is not increased, but there appear only additional special functions. Given are calculation results of the fuel channel of LWGR type reactor by the program, realizing linear approximation of neutron flux