Sentence examples for by the hypergeometric function from inspiring English sources

Equation (27) is a differential equation satisfied by the hypergeometric function.

In this paper, we introduce a new class of multivalent functions by using a generalized integral operator defined by the hypergeometric function.

In order to avoid numerical instability of classical Krawtchouk polynomials caused by the hypergeometric function, a set of normalized polynomials of Krawtchouk has been mentioned in [17] by the following formula: bar{k}_{n}(x p,N-1)=k_{n}(x p,N-1)sqrt{frac{w_{k}(x;p,N-1)}{rho_{k}(n;p,N-1)}}.

In order to avoid numerical instability of classical Tchebichef polynomials caused by the hypergeometric function in Eq. (1), a set of normalized Tchebichef polynomials has been introduced by Mukundan et al. in [16] by the following formula: bar{t}_{n}(x N =frac{t_{n}(x N)}{beta(n,N }, (6).

where 2 F 1 is the hypergeometric function defined by begin{array}rcl@_{2}F_{1} (a, b; c; x) = frac {Gamma (c)} {Gamma (a)Gamma (b)} sum_{j=0}^{infty} frac{Gamma (a+j Gamma(b+j)} {Gamma (c + j)},frac{x^{j}}{j!},, end{array}.

So for a given gene found in M species, the hypergeometric function provides the probability by random chance that the gene is found in m species which contain the COG and are also positive in the laboratory test.

where is the hypergeometric function, whose integral form is given by (20).

The hypergeometric function of a real variable is computed for arbitrary real parameters.

The transformation theory of the hypergeometric function is used to obtain rapidly convergent power series.

where F is the hypergeometric function.

where is the Euler constant and is the hypergeometric function.