Title
Extension of Frahm formulas for ∂i∂i(1/r)
Document Type
Article
Publication Date
8-1-2013
Abstract
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
First Page
237
Last Page
245
Recommended Citation
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://repository.lsu.edu/mathematics_pubs/281