Connection Matrices Associated with the Generalized Hypergeometric Function 3F2

Subclasses of Bi-Univalent Functions Associated with Generalized Hypergeometric Function

In this paper, we have introduced and investigated two new subclasses of the function class Δ of bi-univalent functions defined in the open unit disk, which are associated with the generalized Hypergeometric function. Furthermore, we find estimates on the Taylor-Maclaurin coefficient | a2 | and | a3 | for the functions belonging to these new classes.

3f2 Hypergeometric Series and Periods of Elliptic Curves

We express the real period of a family of elliptic curves in terms of classical hypergeometric series. This expression is analogous to a result of Ono which relates the trace of Frobenius of the same family of elliptic curves to a Gaussian hypergeometric series. This analogy provides further evidence of the interplay between classical and Gaussian hypergeometric series.

Inclusion properties of certain classes of meromorphic functions associated with the generalized hypergeometric function

Let Σp denote the class of functions normalized by f(z) = z−p + ∞ ∑ n=1 anz n−p (p ∈ N), which are analytic and p-valent in 0 < |z| < 1. Making use of a linear operator, which is defined here by the generalized hypergeometric function, we introduce some new subclasses of the meromorphically p-valent function class Σp and investigate their inclusion relationships. Mathematics Subject Classificat...

On certain classes of meromorphically multivalent functions associated with the generalized hypergeometric function

In the present paper, we investigate several inclusion relationships and other interesting properties of certain subclasses of meromorphically multivalent functions which are defined here by means of a linear operator involving the generalized hypergeometric function. Some interesting applications on Hadamard product concerning this and other classes of integral operators are also considered.

On Hypergeometric-type Generating Relations Associated with the Generalized Zeta Function