How do I write out the following equation:
$\Delta S = \sqrt{\sum_{a=\alpha,\alpha'}^{}\sum_{b=\beta,\beta'}^{}\Delta E(a,b)^2}$
I guess what's throwing me off here is:
I) there is no upper bound on either sigma
II) I don't know how to interpret a notation such as $a=\alpha,\alpha'$
In general, the notation $$\sum_{P(x)}f(x)$$ usually means the sum of $f(x)$ for values of $x$ where $P(x)$ is true. So for your case, $$\sum_{a=\alpha,\alpha'}\sum_{b=\beta,\beta'}\Delta E(a,b)^2=\Delta E(\alpha,\beta)^2+\Delta E(\alpha',\beta)^2+\Delta E(\alpha,\beta’)^2+\Delta E(\alpha',\beta')^2$$ is probably the intended meaning.