Results 181 to 190 of about 97,549 (210)
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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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Extended hypergeometric and confluent hypergeometric functions
Applied Mathematics and Computation, 2004An extension of the beta function by introducing an extra parameter, which proved to be useful earlier, is applied here to extend the hypergeometric and confluent hypergeometric functions. Since the latter functions contain many of the familiar special functions as sub-cases, this extension is expected to prove to be useful.
M. Aslam Chaudhry +3 more
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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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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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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
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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1999
Almost all of the elementary functions of mathematics are either hypergeometric or ratios of hypergeometric functions. A series Σ c n is hypergeometric if the ratio c n +1 / c n is a rational function of n . Many of the nonelementary functions that arise in mathematics and physics also have representations as hypergeometric series.
Ranjan Roy +2 more
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Almost all of the elementary functions of mathematics are either hypergeometric or ratios of hypergeometric functions. A series Σ c n is hypergeometric if the ratio c n +1 / c n is a rational function of n . Many of the nonelementary functions that arise in mathematics and physics also have representations as hypergeometric series.
Ranjan Roy +2 more
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Generalized Hypergeometric Functions
1998Abstract The special properties associated with the hypergeometric and confluent hypergeometric functions have spurred a number of investigations into developing functions even more general than these. Some of this work was done in the nineteenth century by Clausen, Appell, and Lauricella (among others), but much of it has occurred ...
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Female erectile tissues and sexual dysfunction after pelvic radiotherapy: A scoping review
Ca-A Cancer Journal for Clinicians, 2022Deborah C Marshall +2 more
exaly
The Confluent Hypergeometric Functions
1998Abstract Whereas Gauss was largely responsible for the systematic study of the hypergeometric function, E. E. Kummer (1810-1893) is the person most associated with developing properties of the related confluent hypergeometric function. Kummer published his work on this function in 1836,* and since that time it has been commonly referred ...
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