Results 191 to 200 of about 5,795,833 (227)

Geometric Properties of Generalized Hypergeometric Functions

The Ramanujan Journal, 1997
The authors determine conditions on the parameters \(a_j>0\) \((j= 1,2,3)\) and \(b_j> 0\) \((j= 1,2)\) so that the function \[ z{_3F_2}(a_1, a_2,a_3; b_1,b_2; z) \] is univalent in the open unit disk \(U\), \({_3F_2}\) being the Clausenian hypergeometric function.
Ponnusamy, S., Sabapathy, S.
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Generalized Hypergeometric Function of Unit Argument

Journal of Mathematical Physics, 1970
Two summation theorems are given for the terminating generalized hypergeometric function pFp−1, for arbitrary p, with certain restrictions on the parameters.
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Classes of analytic functions associated with the generalized hypergeometric function

Applied Mathematics and Computation, 1999
Using the generalized hypergeometric function, the authors introduce and study a class of analytic functions with negative coefficients. Coefficients estimates, distortion theorems, extreme points, and the radii of convexity and starlikeness for this class are given. Relevant connections of these results with those in several earlier investigations are
Jacek Dziok, H. M. Srivastava 0001
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A new generalization of q-hypergeometric function

Bollettino dell'Unione Matematica Italiana, 2015
The author introduces a so-called \(q\)-\(\ell\)-\(\Psi\) function by \[ \Psi\left[\begin{matrix} a; & b; & q; & z\\ c; & \left( d:\ell\right) ; & & \end{matrix} \right] =\sum_{n=0}^{\infty}\frac{\left( a;q\right) _{n}\left( b;q\right) _{n}}{\left( c;q\right) _{n}\left( d;q\right) _{n}^{\ell n}}\frac{z^{n} }{\left( q;q\right) _{n}}, \] where ...
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On the Hankel Transform of Generalized Hypergeometric Functions

Journal of the London Mathematical Society, 1946
Not ...
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Lie Theory and Generalizations of the Hypergeometric Functions

SIAM Journal on Applied Mathematics, 1973
In this paper we use the differential recurrence relations satisfied by the ${}_2 F_1 $ and their generalizations the${}_p F_q $ and Lauricella functions to associate a Lie algebra (dynamical symmetry algebra) with each of these families of special functions. We demonstrate that the representation theory of the Lie algebras yields a variety of addition
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General Linear Transformations of Hypergeometric Functions

Mathematical Notes, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Extension of Pochhammer symbol, generalized hypergeometric function and τ-Gauss hypergeometric function

Analysis
Abstract We introduce new extension of the extended Pochhammer symbol and gamma function by using the extended Mittag-Leffler function. We also present extension of the generalized hypergeometric function as well as some of their special cases by using this extended Pochhammer symbol.
Komal Singh Yadav, Bhagwat Sharan, Ashish Verma   +2 more
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Generalized Hypergeometric Functions

Mathematics of Computation, 1966
Y. L. L., Lucy Joan Slater
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GENERALIZED HYPERGEOMETRIC FUNCTIONS

Journal of the London Mathematical Society, 1968
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