Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions
نویسندگان
چکیده
منابع مشابه
Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions
We describe a uniform way of obtaining basic hypergeometric functions as limits of the elliptic beta integral. This description gives rise to the construction of a polytope with a different basic hypergeometric function attached to each face of this polytope. We can subsequently obtain various relations, such as transformations and three-term relations, of these functions by considering geometr...
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Introduction. The wonderful book by Andrews, Askey, and Roy [2] is mainly devoted to special functions of hypergeometric type – to the plain and q-hypergeometric series and integrals. Shortly before its publication, examples of a third type of such functions, related to elliptic curves, began to appear. A systematic theory of elliptic hypergeometric functions was constructed in 2000-2004 over a...
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In the present paper, we have established sufficient conditions for Gaus-sian hypergeometric functions to be in certain subclass of analytic univalent functions in the unit disc $mathcal{U}$. Furthermore, we investigate several mapping properties of Hohlov linear operator for this subclass and also examined an integral operator acting on hypergeometric functions.
متن کاملMapping Properties of Basic Hypergeometric Functions
It is known that the ratio of Gaussian hypergeometric functions can be represented by means of g -fractions. In this work, the ratio of q -hypergeometric functions are represented by means of g -fractions that lead to certain results on q -starlikeness of the q -hypergeometric functions defined on the open unit disk. Corresponding results for the q -convex case are also obtained.
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ژورنال
عنوان ژورنال: Symmetry, Integrability and Geometry: Methods and Applications
سال: 2009
ISSN: 1815-0659
DOI: 10.3842/sigma.2009.059