"A function of a variable quantity is an analytic expression composed in any way whatsoever of the variable quantity and numbers or constant quantities."

The rules were developed by John C. Slater in an attempt to construct simple analytic expressions for the atomic orbital of any electron in an atom.

Since an analytic expression for the gradient is not available, one must rely on a noisy estimate.

Additionally, there is an analytic expression for which is infinite in extent, and thus not physically realizable.

Unlike the broader analytic expressions, the closed-form expressions do not include infinite series or continued fractions; neither includes integrals or limits.

Ford observed the passing cloud sculpture with a fixed, analytic expression.

He defined the "Hernquist Profile", which is an analytic expression for the distribution of dark matter in galaxies.

Carnby had noted my surprise, and was watching me with a keen, analytic expression which I found impossible to fathom.

The above approximation can be used to derive an analytic expression for the ratio of the mean intensity to the central intensity.

Inserting the formulas for the prior, the likelihood, and the posterior and simplifying the resulting expression leads to the analytic expression given above.