What is the term for an asterisk in combination with a variable? This question could likely be phrased better, but I'm not sure how to better describe it.
In calculus, when studying sigma notation, especially with Riemann sums, you often see something like this:
$$A = \sum_{k=1}^{n} f(\color{red}c_k^\color{red}*)\Delta x$$
I know that in the specific case of Riemann sums, it means that you are to select any $c_k$ in the interval $[c_{k-1}, c_k]$ and evaluate $f(c_k)$ as part of the sum. But I'm wondering about the meaning of the asterisk notation in general.
My question: what is the name for (or how to you pronounce) the $\color{red}c^\color{red}*$ term?
More generally, what do you call a variable or term that has an asterisk above it like, that? And, what is the mathematic meaning of the asterisk, in a general sense?
 A: I would pronounce it "c-k-star".  The meaning is just that these are new values used to approximate the previous values, so like the $c_{1}, \ldots, c_{n}$ define regions of the number line, and $c_{k}^{*}$ is not one of these values, but it is used to essentially approximate $c_{k}$ (being between $c_{k-1}$ and $c_{k}$). There are several ways to choose this value, either a left ($c_{k}^{*} = c_{k-1}$) or right ($c_{k}^{*} = c_{k}$) endpoint of the interval, or a mid point ($c_{k}^{*} = \frac{c_{k-1}+c_{k}}{2}$), or really it can be chosen arbitrarily (it will all come out the same once you take the limit over a partition refinement).
A: To answer the second part of your question: the asterix has a lot of different meanings. Sometimes it is just a new variable name (like in your example) that should be explained in the text surrounding the formula. Often, this will be some extremum (in case of Riemann sums, that is yet another choice).
In other contexts, it can also denote the complex conjugate of a complex number, the adjoint of an operator in a Hilbert space, the dual of a linear operator, and very commonly the pullback operator associated to some function. And these are certainly not all meanings.
