Sentence examples for definition of the generating from inspiring English sources

If we use n weights (w_{1}, ldots, w_{n}) in the definition of the generating functions of Euler polynomials, then the symmetric group (S_{n}) naturally acts on a prescribed set of generating functions of the Euler polynomials.

Each of the active interfering macro-BSs transmits with the same power P P. Again, using the definition of the generating functional for the PPP, we can write {mathrm{mathcal{L}}}_{I_{mathrm{MB}}}(s)= exp left{-{mathrm{E}}_Gleft[{displaystyle underset{0}{overset{infty }{int }}}left 1- exp left -s{P}_PG{L}^{-alpha}right)right){left -s{P}_PG{L}^{-alpha}rightght}.

From the definition of the generating function it follows that R (x,   t ) = ∂ ω ϕ ω (x,   t ) | ω = 0. Differentiating Equation (5) w.r.t.

Each of the active interfering macro-BSs transmits with the same power P M. Again, using the definition of the Generating functional for the PPP, we can write {mathrm{mathcal{L}}}_{I_{MB}}(s)= exp left{-{mathrm{E}}_Gleft[{displaystyle underset{0}{overset{infty }{int }}}left 1- exp left -s{P}_MG{L}^{-alpha}right)right){left -s{P}_MG{L}^{-alpha}rightght}.

This follows easily from the definition of the generating rule (Definition 2.4).

Now we give some basic definitions of the generating space of a b-quasi-metric family.

This leads to the formal definition of the probability generating function: f ( q ) = E [ q X ] = p 0 + p 1 q + p 2 q 2 + p 3 q 3 … p n q n = ∑ k = 0 n p k q k. (1).

end{aligned} Noting that intmathcal{D}eta(t)e^{inttilde{x}(t)eta(t),dt -S_{eta}[eta(t)]} = e^{W[tilde{x}(t)]} is the definition of the cumulant generating functional for (eta(t)), we find that the path integral can be written as Pbigl[x t) | y, t_{0}bigr] = intmathcal{D}eta(t mathcal{D} tilde{x}(t) e^{-inttilde{x}(t) (dot{x}(t -f x,t -f xlta(t-t_{0})),t -ydelta t-t_{t)]}.

First, we give the following new definition of the solution generated by impulses.

In Eq. 5, we can find the formal definition of the tree generated by create_tree, knowing that (s_{p} odot e^_{p}~=~1, s_{p} odot kappa _{p}~=~1 forall s_{p} in s).

into the sum of a right-continuous martingale M and an adapted, natural, increasing, integrable process A. The process A is then called the compensator of H. On the other hand, from the definition of the potential generated by an increasing process (see Definition C.1), the process L =G+K^{w} (24). is a martingale.