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EXPANSIONS OF HYPERGEOMETRIC FUNCTIONS
The Quarterly Journal of Mathematics, 1942Not ...
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Recursive subdivision and hypergeometric functions
Proceedings SMI. Shape Modeling International 2002, 2003We 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, 1997The 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
2001The 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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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 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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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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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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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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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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Hypergeometric function representations
Proceedings of the 1996 international symposium on Symbolic and algebraic computation - ISSAC '96, 1996openaire +1 more source
Recurrences for hypergeometric functions
2003Summary: Many of the known recurrences for the hypergeometric functions of several variables involve more than two parameters. A method is developed which allows a search of the functions for recurrences which involve only a specific number of the parameters, in particular, two parameter recurrences.
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Asymptotic expansions and inequalities for hypergeometric function
Mathematika, 1997Saminathan Ponnusamy, M Vuorinen
exaly