Extension of Frahm formulas for ∂i∂i(1/r)
We prove the formula ∂*2(r-1/∂x i∂xj = (3xixj- ∂ijr2)pf(r-5)+4π(∂ij- 4ninj)∂*, for the second order thick derivatives of r-1 in R3, where S. is a thick delta of order 0. This formula generalizes the well known Frahm formula for the distributional derivatives of r"1, and provides an alternative to the extended formula given by J. Franklin in "Comment on 'Some novel delta-function identities' by Charles P Frahm (Am. J. Phys. 51 826-9 (1983))," Am. J. Phys. 78 1225-26 (2010). © 2013 Allahabad Mathematical Society.
Publication Source (Journal or Book title)
Indian Journal of Mathematics
Yang, Y., & Estrada, R. (2013). Extension of Frahm formulas for ∂i∂i(1/r). Indian Journal of Mathematics, 55 (2), 237-245. Retrieved from https://digitalcommons.lsu.edu/mathematics_pubs/281