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

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