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The phrase "as the characteristic function of the" is correct and usable in written English.
It can be used in mathematical or statistical contexts, particularly when discussing functions that describe the distribution of random variables.
Example: "The probability distribution can be represented as the characteristic function of the random variable."
Alternatives: "as the defining function of the" or "as the distribution function of the".
Exact(2)
Then define s → j ( i ) as the characteristic function of the set.
As the characteristic function of the sum of two independent variables is the product of their characteristic functions, and each variable here has the characteristic function 1 − μ + μ cos ω, the characteristic function of Δ is (1 − μ + μ cos ω ) 2 t.
Similar(58)
Denote the characteristic function of the interval.
E.g., this quasipolynomial results as the characteristic function of PID controlled linear time delay systems.
Then each binary number may be viewed as the characteristic function of a finite subset of natural numbers.
where is the characteristic function of defined as (1.3).
As a function of M, Equation (10) represents the characteristic function of x ^ m ≜ ℜ { x m }.
where is the characteristic function of.
For any the function denotes the characteristic function of.
This equation is known as boundary characteristic function of item i for category k.
Suppose you wish to know the value of a specific Turing-uncomputable characteristic function, such as the halting function for Turing machines, for its nth argument.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com