It arises in the least squares approximation of arbitrary functions by polynomials.

When a variable belongs to the field of real numbers, messages can be arbitrary functions, and special care needs to be taken in their representation.

The meanings of the three arbitrary functions, which depend on only, are:

The function can be employed for arbitrary functions merely by employing the appropriate expressions.

So for many purposes, one can replace arbitrary functions on by Morse functions.

It has been shown that it can be extended beyond the context of images to arbitrary functions.

Code documents are often organized into a reference guide style, allowing a programmer to quickly look up an arbitrary function or class.

The user supplies an arbitrary function, as a delegate or lambda expression, which projects the data members.

For an arbitrary function the orthogonality relationship can be used to expand :

The second observation is that, once the level surfaces are known, all solutions can then be given in terms of an arbitrary function.