Results 221 to 230 of about 94,918 (265)

Extended hypergeometric and confluent hypergeometric functions

Applied Mathematics and Computation, 2004
The functions under consideration are the extended Gaussian hypergeometric function \[ F_p(a,b;c,z)= {1\over B(b,c- b)} \int^1_0 t^{b-1}(1- t)^{c-b-1}(1- zt)^{-a}\exp\Biggl[-{p\over t(1- t)}\Biggr]\,dt \] and its confluent counterpart \(\Phi_p(b;c;z)\) with \(\exp(zt)\) in place of \((1- zt)^{-a}\). The authors discuss differentiation with respect to \(
Chaudhry, M. Aslam, Qadir, Asghar, Srivastava, H. M., Paris, R. B.   +3 more
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Operator Hypergeometric Functions

Journal of Mathematical Sciences, 2023
The paper deals with differential equations \[ Du=Au\tag{1} \] with a differential operator \(D\) and unbounded operator coefficients \(A\). If the case when the Cauchy problem for equation (1) is uniformly well-posed then its solution can be represented via transformation operator.
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PATH HYPERGEOMETRIC FUNCTIONS

Journal of Algebra and Its Applications, 2007
Under a certain condition, we find the explicit formulas for the trace functions of certain intertwining operators among gl(n)-modules, introduced by Etingof in connection with the solutions of the Calogero–Sutherland model. If n = 2, the master function of the trace function is exactly the classical Gauss hypergeometric function.
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Multivariable Hypergeometric Functions

2001
The goal of this lecture is to present an overview of the modern developments around the theme of multivariable hypergeometric functions. The classical Gauss hypergeometric function shows up in the context of differential geometry, algebraic geometry, representation theory and mathematical physics.
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The hyperbolic–hypergeometric functions

Journal of Mathematical Physics, 2001
In this work we present a new function to represent the approximate solution of a system of three charged particles. This function is based on an extension to two variables of the confluent hypergeometric function 1F1 of Kummer and can be obtained using a method similar to that used by Appell and Kampé de Fériet.
Gasaneo, G., Colavecchia, F. D., Otranto, S., Garibotti, C. R.   +3 more
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Zeros of Hypergeometric Functions

Computational Methods and Function Theory, 2001
Here it is shown that the hypergeometric function \(F(a,b;b+1;z)\) has no zeros in a specified half-plane for certain ranges of parameters. It is also shown that the zeros of the hypergeometric polynomials \(F(-n,kn+ \ell+1; kn+ \ell+2;z)\) cluster on one loop of a specified lemniscate. Other results then follow from quadratic relations.
Boggs, Kathryn, Duren, Peter
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ON q-HYPERGEOMETRIC FUNCTIONS

Far East Journal of Mathematical Sciences (FJMS), 2017
Summary: In this article, we study some results on meromorphic functions defined by \(q\)-hypergeometric functions. In addition, certain sufficient conditions for these meromorphic functions to satisfy a subordination property are also pointed out. In fact, these results extend known results of starlikeness, convexity, and close to convexity.
Challab, K. A., Darus, M., Ghanim, F.
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Extended Multivariable Hypergeometric Functions

2019
In this chapter, we define an extension of multivariable hypergeometric functions. We obtain a generating function for these functions. Furthermore, we derive a family of multilinear and multilateral generating functions for these extended multivariable hypergeometric functions.
Erkuş-Duman, Esra, Düzgün, Düriye
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EXPANSIONS OF HYPERGEOMETRIC FUNCTIONS

The Quarterly Journal of Mathematics, 1942
Not ...
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Computing the Hypergeometric Function

Journal of Computational Physics, 1997
The Gauss hypergeometric function \({}_2F_1(a,b;c;x)\) is computed for real values of the variables \(a, b, c\) and \(x\). Transformation formulas are used to give a suitable \(x-\)interval for the power series. Great care is taken for the divergences that occur for certain values of \(a, b\) and \(c\) in the transformations.
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