Sentence examples for binomial identity from inspiring English sources

Recently, Jonathon [4] gave a simple and interesting probabilistic proof of the above binomial identity, and he further extended this binomial identity based on the probabilistic method.

Below we give an extension of binomial identity (7) and deduce some new binomial identities.

Every choice of the function f and the random variable T in Theorem 2.1 gives us a different binomial identity.

Specifically, by making use of the following well-known binomial identity k k - 1 i - 1 = i k i ( k ≥ i ≥ 1 ).

Setting (r=1) and (theta=beta) in (18) and defining the empty sum (sum_{j=1}^{0}=0), we have the following new binomial identity.

Setting (r=1) and (theta=beta) in (10) of Theorem 4 and (r=2) and (theta=beta) in (11) of Theorem 4, we have the following new binomial identity.

Some old and new binomial identities are obtained.

We can obtain many old and new binomial identities.

There is much literature about the binomial identities, we refer the readers to [7 17].

As some applications, some old and new binomial identities are obtained.

A generalized linear model (GLM) was used to determine the effects of species and prey availability (limited, ample) on the juvenile survival probabilities (binomial distribution, identity link function) and body size (normal distribution, identity link function) of the males used in the experiments.