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.