Are Capital-sigma summation notation and Einstein summation notation the same thing? If not, what is the difference?

Question

There are two Wikipedia pages describing summation notation: Capital-sigma summation notation and Einstein summation notation.

Are these two notations the same? If not, what is the difference?

Answer 1

As the Wikipedia entry explains, Einstein notation is a short-form way of expressing sums. In Einstein notation, contrary to Sigma notation, we omit the summation symbol $\Sigma$.

$$ \underset{\text{Sigma notation}}{\sum _{i=1}^{3}c_{i}x^{i}} \longrightarrow \underset{\text{Einstein notation}}{c_{i}x^{i}} $$