TL;DR
This paper develops techniques to compute the scalar functional determinant on the Euclidean d-ball with Dirichlet and Robin boundary conditions, using large mass asymptotics and Watson-Kober summation, providing explicit formulas for dimensions 2 and 4.
Contribution
It introduces a direct method for calculating scalar functional determinants on the Euclidean ball with Robin boundary conditions, including explicit formulas for specific dimensions.
Findings
Derived general formulas for scalar determinants with Robin conditions
Obtained explicit results for dimensions 2 and 4
Utilized Watson-Kober summation in the analysis
Abstract
Techniques are presented for calculating directly the scalar functional determinant on the Euclidean d-ball. General formulae are given for Dirichlet and Robin boundary conditions. The method involves a large mass asymptotic limit which is carried out in detail for d=2 and d=4 incidentally producing some specific summations and identities. Extensive use is made of the Watson-Kober summation formula.
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