Zeta function determinant of the Laplace operator on the $D$-dimensional ball

Abstract

We present a direct approach for the calculation of functional determinants of the Laplace operator on balls. Dirichlet and Robin boundary conditions are considered. Using this approach, formulas for any value of the dimension, $D$, of the ball, can be obtained quite easily. Explicit results are presented here for dimensions $D=2,3,4,5$ and $6$.