A question about the notation of $_\lambda\varphi$

Question

I've seen such a notation.

The sequence $\left\{\lambda_1,\lambda_2,\lambda_3,\cdots \lambda_n\right\}$ is given, where $\lambda_i\in\mathbb{R}$ and $i=1,2,3\cdots$

This sequence is given by the law of $\varphi$ of the sequence of $\lambda$ numbers.

There is such a notation:

$$ _\lambda\varphi(z):= \lambda_z$$ where $z\in\mathbb{Z_+}$ or $z=1,2,3\cdots$

The author says: The meaning of $_\lambda\varphi$ the sequence of $\lambda$ numbers is given by law of $\varphi$.

I have not seen this notation used before, and would like to understand:

1. is this notation commonplace, or is it peculiar to just this author? By way of elaboration, I'm curious as to whether I would be expected to recognise this notation by people working the field if they showed it without explanation.

2. how common is it for an author to define new notation? Am I always going to be finding new notation for things I thought I understood?