On some new contiguous relations for the Gauss hypergeometric function with applications
نویسندگان
چکیده
منابع مشابه
Contiguous relations of hypergeometric series
The 15 Gauss contiguous relations for 2F1 hypergeometric series imply that any three 2F1 series whose corresponding parameters differ by integers are linearly related (over the field of rational functions in the parameters). We prove several properties of coefficients of these general contiguous relations, and use the results to propose effective ways to compute contiguous relations. We also di...
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ess as: 2), http: athemat s.2012.0 Abstract Two Gauss functions are said to be contiguous if they are alike except for one pair of parameters, and these differ by unity. Contiguous relations are of great use in extending numerical tables of the function. In this paper we will introduce a new method for computing such types of relations. a 2012 Egyptian Mathematical Society. Production and hosti...
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We give a basic introduction to the properties of Gauss’ hypergeometric functions, with an emphasis on the determination of the monodromy group of the Gaussian hyperegeometric equation. Initially this document started as an informal introduction to Gauss’ hypergeometric functions for those who want to have a quick idea of some main facts on hypergeometric functions. It is the startig of a book ...
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The Gauss hypergeometric function 2F1(a, b, c; z) can be computed by using the power series in powers of z, z/(z − 1), 1 − z, 1/z, 1/(1 − z), (z − 1)/z. With these expansions 2F1(a, b, c; z) is not completely computable for all complex values of z. As pointed out in Gil, et al. [2007, §2.3], the points z = e±iπ/3 are always excluded from the domains of convergence of these expansions. Bühring [...
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In recent years, several interesting families of generating functions for various classes of hypergeometric and generalized hypergeometric functions in one, two and more variables were investigated systematically. Here, in this sequel, we aim at establishing several (presumably) new generating relations for the generalized Gauss type hypergeometric functions which are introduced by means of som...
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ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 2011
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2010.12.008