Sentence examples for generating function can be from inspiring English sources

As a generating function, can be used in generally the following formula [10]: (2.13).

Some structural properties of the new family such as the ordinary and incomplete moments and generating function can be determined from well-established properties of the Exp-G distribution.

The generating function can be accurately approximated in regimes where ϕ ω is small and the non-linear term in Equation (5) can be neglected, as well as the regime of large enough x where ϕ 'saturates': ϕ ω (x,   t ) ≈ x, see (Neher and Hallatschek, 2013).

The Hermite-Gaussian generating function can be expressed by its operator equivalent as (4).

This equation for the generating function can be solved numerically or analytically in limiting cases.

These mean that generating functions can be dealt with systematically in the compact case.

The expansion of the generating functions can be done by power series expansion (PSE).

Then one can investigate whether some generating functions can be applied to it and study what kind of new properties can be obtained by considering special generating functions.

If instead the moments are known, the extremal distributions can be found and the roots of their generating functions can be solved to find the bounds on extinction.

In addition to the material given in the above paragraph, one can also investigate whether the set, say B, of this minimal number of generating functions can be a generating set of this type of functions.

Probability generating functions can be written as y ( x, t ) = ∑ i = 0 n P i ( t ) x i = P 0 ( t ) + P 1 ( t ) x + P 2 ( t ) x 2 + ⋯ + P n ( t ) x n. (8).