ROBIN CONDITIONS ON THE EUCLIDEAN BALL

Techniques are presented for calculating directly the scalar functiona l determinant on the Euclidean d-ball. General formulae are given for Dirichlet and Robin boundary conditions when d is even and the field i s massless. The method involves a large mass asymptotic limit which is carried out in detail for d = 2 as an exercise, incidentally producin g some specific summations and identities. Extensive use is made of th e Watson-Kober summation formula. The calculation of the finite-mass d eterminant is also briefly considered.