# B Einstein summation notation, ambiguity?

#### Hiero

If I see $f(x_ie_i)$ I assume it means $f(\Sigma x_ie_i)$ (summing in the domain of f) but what if I instead wanted to write $\Sigma f(x_ie_i)$ (summing in the range)?

Is there a way to distinguish between these in Einstein’s summation notation?

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#### PAllen

This is an odd case, but I think if you want the latter, in a context where Einstein summation is implied, you have to write it explicitly, overriding the convention. Only first case is handled by the summation convention.

#### Dale

Mentor
Is there a way to distinguish between these in Einstein’s summation notation?
So $f(\Sigma x^{\mu}e_{\mu})$ is $f(x^{\mu}e_{\mu})$ and $\Sigma f(x^{\mu}e_{\mu})$ is $f(x^{\mu}e_{\nu})\delta^{\nu}_{\mu}$

• sophiecentaur, PeroK and Hiero

#### Hiero

So $f(\Sigma x^{\mu}e_{\mu})$ is $f(x^{\mu}e_{\mu})$ and $\Sigma f(x^{\mu}e_{\mu})$ is $f(x^{\mu}e_{\nu})\delta^{\nu}_{\mu}$
Oh wow, that’s clever! Thanks for the insight.

• Dale