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For questions about mathematical notation, i.e. the symbols used to represent mathematical objects and operations.

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What is the meaning of big-O of a random variable?

I excerpt it below: screenshot of the book In the excerpt, the big-O notation $O(\xi^3)$ in equation (5.130.1) and (5.130.2) fits my understanding because $\xi$ is the variable of the function being expanded … But I don't understand the big-O notation $O(\xi^3)$ in equation (5.130.3), because the thing being expanded here, $\widetilde E$, is not a function of $\xi$. …