Tables of Racah Coefficients presents a compilation of tables of Racah coefficients. Racah coefficients appear and are widely used in a number of problems in quantum mechanics; in the theory of spectra of complex atoms and nuclei; in the theory of angular distributions of nuclear reactions; in the theory of angular correlations of decay particles; and many other problems where the sums of products of three or more Clebsch-Gordan coefficients occur. In compiling tables of Racah coefficients certain conditions can be imposed on the indices, which follow from the symmetry relations. Only those coefficients are given which satisfy these conditions. The present tables consist of three parts. The first part gives Racah coefficients in which the first four indices are half-integers, and the other two integers. The second gives Racah coefficients with integer indices. The third gives Racah coefficients in which the three indices, a, c, e are half-integers, and the other three are integers.

A general discussion of applying these formulas to the numerical solution of partial differential equations is made. An illustrative problem with function value given on a circular boundary is solved by both relaxation and matrix methods. Similar applications to compressible flow past isolated and cascade airfoils, through turbomachines, and temperature and stress distribution is cooled turbine blades is indicated.