# Finding Einstein notation version of a given flow equation

geojenny

## Homework Statement

This is from lecture, not a homework problem per se. But I need assistance.

The problem was to write this form of a flow equation in Einstein's notation:

## Homework Equations

$\frac{\partial }{ \partial x_1}(K_1 \frac{\partial h}{\partial x_1}) + \frac{\partial }{ \partial x_2}(K_2 \frac{\partial h}{\partial x_2})+ \frac{\partial }{ \partial x_3}(K_3 \frac{\partial h}{\partial x_3}) = 0$

Where $K_1, K_2, K_3$ are from a diagonalized form of the K tensor.

## The Attempt at a Solution

The given solution is $\frac {\partial} {\partial x_i} (K_i \frac {\partial h} { \partial x_i}) = 0$, where i = 1,..,3

Which is supposed to be related to
$\frac {\partial} {\partial x_i} (K_{ij} \frac {\partial h } { \partial x_j }) = 0$ when $K_{ij} = 0$ if i ≠ j

I'm confused because there's an index repeated twice (appears three times), which I learned is bad in a different class. Is there a better way to write this equation?

geojenny
Does anybody have any idea? This isn't a homework question, and my engineering professor said to simply replace all three subscripts with an i to get Einstein's summation convention, and a repeated subscript implies summation.

However, I'm pretty sure this is incorrect because I have independently learned that the subscript can only be repeated once (appear twice). Is this really a correct way to express the equation in Einstein's notation?