Spinors and forms on the ball and the generalized cone

A method is presented, and used, for determining any heat-kernel coefficien t for the form-valued Laplacian on the D-ball as an explicit function of di mension and form order. The calculation is offerred as a particular applica tion of a general technique developed earlier for obtaining heat-kernel coe fficients on a bounded generalized cone which involves writing the sphere a nd ball xi-functions, and coefficients, in terms of Barnes xi-functions and generalized Bernoulli polynomials. Functional determinants are computed. S pinors are also treated by the general method.