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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.   +3 more
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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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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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EXPANSIONS OF HYPERGEOMETRIC FUNCTIONS

The Quarterly Journal of Mathematics, 1942
Not ...
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Recursive subdivision and hypergeometric functions

Proceedings SMI. Shape Modeling International 2002, 2003
We describe a method for efficient calculation of coefficients for subdivision schemes. We work on the unit sphere and we express the z-coordinate of all the existing points as power series in the variable cos /spl theta/. Any linear combination of them is also a power series in cos /spl theta/ and, by solving a linear system, we determine the linear ...
Ioannis P. Ivrissimtzis   +2 more
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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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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 hypergeometric function

1966
The function represented by the infinite series \(\sum\limits_{n = 0}^\infty {\frac{{{{(a)}_n}{{(b)}_n}}}{{{{(c)}_n}}}\frac{{{z^n}}}{{n!}}} \) within its circle of convergence and all the analytic continuations is called the hypergeometric function 2 F 1(a, b; c;z).*
Wilhelm Magnus   +2 more
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The Hypergeometric Function

1998
Abstract Because of the many relations connecting the special functions to each other, and to the elementary functions, it is natural to inquire whether more general functions can be developed so that the special functions and elementary functions are merely specializations of these general functions.
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The Hypergeometric Function

2009
9.1 Introduction Because of the many relations connecting the special functions to each other, and to the elementary functions, it is natural to inquire whether more general functions can be developed so that the special functions and elementary functions are merely specializations of these general functions. General functions of this nature have in
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