Large parameter cases of the Gauss hypergeometric function
نویسندگان
چکیده
منابع مشابه
Large Parameter Cases of the Gauss Hypergeometric Function
We consider the asymptotic behaviour of the Gauss hypergeometric function when several of the parameters a, b, c are large. We indicate which cases are of interest for orthogonal polynomials (Jacobi, but also Krawtchouk, Meixner, etc.), which results are already available and which cases need more attention. We also consider a few examples of 3F2 functions of unit argument, to explain which dif...
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We obtain asymptotic expansions for the Gauss hypergeometric function F(a+ ε1λ ,b+ ε2λ ;c+ ε3λ ;z) as |λ | →∞ when the ε j are finite by an application of the method of steepest descents, thereby extending previous results corresponding to ε j = 0, ±1 . By means of connection formulas satisfied by F it is possible to arrange the above hypergeometric function into three basic groups. In Part I w...
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In this paper, a computational technique is given to re-obtain the explicit forms of two cases of the Gauss hypergeometric function ) ; , , ( 1 2 x c b a F for 2 / 1 + = a b and 2 / 3 , 2 / 1 = c . Some special identities related to the two aforesaid cases are also introduced. Finally a special Maple package, called FormalPowerSeries (FPS), is used to automatically compute some results given in...
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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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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2003
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(02)00627-1