Comment on `Comment on `Some novel delta-function identities' by Charles P Frahm (Am. J. Phys 51 826--9 (1983))' by J. Franklin (Am. J. Phys 78 1225--26 (2010))
Yunyun Yang, Ricardo Estrada
TL;DR
This paper proves a generalized formula for the second order distributional derivative of 1/r in three-dimensional space, extending Frahm's earlier formulas for such derivatives.
Contribution
It introduces a new, generalized formula for the second order 'thick' distributional derivative of 1/r, expanding upon previous Frahm formulas.
Findings
Derived a formula for the second order 'thick' distributional derivative of 1/r
Generalized Frahm's formulas for distributional derivatives
Enhanced understanding of distributional derivatives in Euclidean space
Abstract
We prove the formula for the second order "thick" distributional derivative of 1/r in 3 dimensional Euclidean space. This formula generalizes the well known Frahm formulas for the distributional derivatives of 1/r.
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Taxonomy
TopicsBayesian Methods and Mixture Models · Statistical Distribution Estimation and Applications · Statistical Methods and Inference