Einstein Tensor Notation: Addition inside a function Main Question
Can I represent addition of multi-dimensional variables in this linear function in Einstein Summation Convention?
$$
f(\mathbf{x} + \mathbf{v})
$$
This didn't seem right $f(x_{\mu}+v_{\mu})$ and nor did $f(x+v)_{\mu}$
More Information...
I am doing an unrelated question on multi-dimensional Taylor Series and I wanted to test my knowledge of compact tensor notation.
My full expression is
$$
   f = f(x_1,\cdots,x_N) = f(\mathbf{r})
   \quad\text{and}\quad
   \mathbf{v} = \left(h_1,\cdots,h_N\right)
   \\
   f( \mathbf{r} + \mathbf{v} ) = 
   \mathbf{v} \cdot \nabla f( \mathbf{r} )
   + \sum^{N}_{n=2} \frac{1}{n!} \left( \mathbf{v} \cdot \nabla \right)^n
   f(\mathbf{r}) + R_N ( \mathbf{r}, \mathbf{v})
$$
I am looking to compactly represent this in tensor notation as I am sure it can be done.

After discussion with a few course mates we came to the conclusion that it should generally be left as the following,
$$
f(\mathbf{x} + \mathbf{v}) = \cdots
$$
with index notation on other relevant terms.
On the topic of taylor series for tensors there is a really interesting treatment of Taylor's Theorem in Tensor Calculus presented in this 1929 paper. 
