Jackson - p. 35 - taylor expansion of charge density

[bjnartowt]

Homework Statement

With a Taylor series expansion of the well-behaved $\rho ({\bf{x'}})$ around ${\bf{x'}} = {\bf{x}}$, one finds the Taylor expansion of the charge density to be,

$\rho ({\bf{x'}}) = \rho ({\bf{x}}) + {\textstyle{1 \over 6}}{r^2}{\nabla ^2}\rho + ...$

Homework Equations

The Attempt at a Solution

This proposed Taylor exapnsion looks correct, except for the 1/6 instead of the 1/2. What gives??

 

[gabbagabbahey]

Homework Statement

With a Taylor series expansion of the well-behaved $\rho ({\bf{x'}})$ around ${\bf{x'}} = {\bf{x}}$, one finds the Taylor expansion of the charge density to be,

$\rho ({\bf{x'}}) = \rho ({\bf{x}}) + {\textstyle{1 \over 6}}{r^2}{\nabla ^2}\rho + ...$

The Attempt at a Solution

This proposed Taylor exapnsion looks correct, except for the 1/6 instead of the 1/2. What gives??

Take a look at this thread.