منابع مشابه
A Note on the 2F1 Hypergeometric Function
The special case of the hypergeometric function 2F1 represents the binomial series (1 + x) = ∑∞ n=0 ( α n ) xn that always converges when |x| < 1. Convergence of the series at the endpoints, x = ±1, depends on the values of α and needs to be checked in every concrete case. In this note, using new approach, we reprove the convergence of the hypergeometric series for |x| < 1 and obtain new result...
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The objective of this paper is to define and study new generalized extended gamma functions. A generalized extended gamma probability density function involving generalized hypergeometric function is also defined. Closed form representations of the generalized gamma functions and the moment generating function are derived in the form of H-function using inverse Mellon transform techniques. Inco...
متن کاملA Note on the Hypergeometric Mean Value
in terms of power means and other related means have precipitated the search for similar bounds for the more general 2F1(α, β; γ; r). In an early paper, B. C. Carlson considered the approximation of the hypergeometric mean values ( 2F1(−a, b; b + c; r)) in terms of means of order t, given by Mt(s, r) := {(1 − s) + s(1 − r)t}1/t. In this note, a refinement of one such approximation is establishe...
متن کاملDifferential inequalities imposed by the extended hypergeometric function
Recently, the generalized hypergeometric function is extended by utilizing the Beta function. Based on this type of function, we introduce a new operator in the open unit disk. The present article investigates some subordination and superordination results for certain normalized analytic functions in the open unit disk, which are acted upon by the generalized Noor integral operator. Some of out...
متن کاملCertain Properties of Extended Wright Generalized Hypergeometric Function
In this paper, we obtain the extended Wright generalized Hypergeometric function using extended Beta function. We also obtain certain integral representations, Mellin transform and some derivative properties of extended Wright generalized Hypergeometric function. Further, we represent extended Wright generalized Hypergeometric function in the form of Laguerre polynomials and Whittaker function.
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ژورنال
عنوان ژورنال: Proyecciones (Antofagasta)
سال: 2019
ISSN: 0717-6279
DOI: 10.22199/issn.0717-6279-2019-03-0037