Sentence examples for cases of the function from inspiring English sources

It is worth noting the following special or limit cases of the function Φ λ, μ ; ν ( z, s, a ).

There are two important special cases of the function E q ( x, a ) e q ( x ) = ∑ n = 0 ∞ x n ( q, q ) n, | x | < 1 (4).

The Hardy-Ramanujan master theorem can be represented in different forms by considering special cases of the function F(s; 0) (see [[2], p. 186]) in the above lemma and in theorems (4.1) and (4.2).

It is worth pointing out that the required number of training frames has not to be very large to achieve a good performance level (in our tests we used about 30 40 training frames), by taking into account also the fact that a single frame usually contains several people clusters at different distances, so it may cover several cases of the function to be learned.

Figure 1, represent a typical case of the function on the right-hand side of (19).

The 'Hill climbing' procedure is developed following the recommendations from [25] and [24], for finding the global extreme in the case of the function of three variables.

However, the general case of the function and its relation with the zeta family does not seem to have been realized so far.

They proved the existence of positive solutions and dead core solutions (vanishing on a subinterval, ) of problem (1.3), and also covered the case of the function approximated by some regular function.

In the case of the function f z) defined and analytic in a certain region involving the interval [0,1], the problem was investigated by Wright [2], Kantorovich [3] and then Bernstein [4].

Control of water access can be seen as a special case of the function described in section 2.1.

Our results are also true for three cases of the potential function V ( x ).