Sentence examples for distribution relations from inspiring English sources

Furthermore, we find distribution relations of generalized twisted Euler numbers and polynomials.

We obtain distribution relations for the -Euler polynomials, and have some identities involving the -Euler numbers and polynomials.

We obtain distribution relations for the -Euler polynomials and have some identities involving -Euler numbers and polynomials.

Thus, the distribution relations for the Genocchi numbers and the Genocchi polynomials for with are obtained as follows (cf. [6]): (3.11).

We obtain distribution relations for the -Bernoulli polynomials and have some identities involving -Bernoulli numbers and polynomials related to the second kind Stirling numbers and -Bernstein polynomials.

Specifically, we generate N times n synthetic random magnitudes m i, i = 1, …, n, distributed according to the GEV distribution (relation (4)).

The optimal distribution relation of the heat-transfer surface areas is also obtained.

Theorem 2.4 (Distribution relation for ).

Therefore, by (12), we obtain the following distribution relation for a Barnes-type Bernoulli polynomial.

The first author et al. [6] obtained the distribution relation for the Genocchi polynomials.

If we substitute (2.7) into (3.12), we get a new relation for the distribution relation of -Genocchi numbers: (3.14).