Sentence examples for generating relation from inspiring English sources

Now, using the weighted function (F_{omega}), we introduce a generalization of the generating relation given in [18], pp.1750-1751 (see also [14]).

But if nothing is known about the generating relation that produces the structure, then the claim that there exists such a structure is vacuous, Newman claimed.

More precisely, the Euler polynomials are defined via the generating relation G E ( x, t ) = 2 e x t e t + 1 = ∑ n = 0 ∞ E n ( x ) t n n !, | t | < π.

Bernoulli polynomials are defined by the following generating relation: G ( x, t ) = t e t − 1 e x t = ∑ n = 0 ∞ B n ( x ) t n n ! ; | t | < 2 π. and Bernoulli numbers B n : = B n ( 0 ) can be obtained by the generating relation t e t − 1 = ∑ n = 0 ∞ B n t n n !. Particularly, B 0 = 1, B 1 = − 1 2, B 2 = 1 6 (3).

Recently, Gabriella Bretti and Paolo E. Ricci defined the two-dimensional Bernoulli polynomials B n ( j ) ( x, y ) ( j ∈ N 2 : = { 2, 3, 4, … } ) via the generating relation G ( j ) ( x, y ; t ) = t e t − 1 e x t + y t j = ∑ n = 0 ∞ B n ( j ) ( x, y ) t n n !, | t | < 2 π. (5).

Recall that the Apostol-Euler polynomials E n ( x ; λ ) are generalized by Luo [21] and given by the generating relation ( 2 λ e t + 1 ) α e x t = ∑ n = 0 ∞ E n α ( x ; λ ) t n n ! ( | t | < π  when  λ = 1 ; | t | < | log |  when  λ ≠ 1 ; 1 α : = 1 ).

The generating relations of a design determine its resolution.

Below we obtain some bilinear generating relations for the weighted extended hypergeometric function (_{2}{F_{1}}).

We prove several two-sided linear generating relations and obtain various series identities for these polynomials.

In this section, we establish some linear and bilinear generating relations for the extended hypergeometric function (F_{p,q}) (9).

A strategy assumes a place that can be circumscribed as proper and thus serve as the basis for generating relations with an exterior distinct from it.