Abstract Ultraspherical polynomial P (λ) n approximations are used in reflected slab criticality calculations for strongly anisotropic scattering. A unique formulation is developed for reflected slab criticality conditions whose special cases are spherical harmonics approximations, Chebyshev polynomial approximations of first and second kind. It is shown in the calculations that all ultraspherical polynomial approximations are equivalent regarding the convergence of the solution of one-speed neutron transport equation for various degrees of anisotropy and cross section parameters. Although some ultraspherical polynomials approximations converge in the mean as the order of approximation is increased and some converge uniformly, they all converge to the same critical thickness which implies their equi-convergence. It is also demonstrated that the first order approximation P (λ) 1 would give the exact critical thickness for a certain value of the parameter λ.