New series expansions of the Gauss hypergeometric function
نویسندگان
چکیده
منابع مشابه
New series expansions of the Gauss hypergeometric function
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 [...
متن کاملGauss’ hypergeometric function
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 ...
متن کاملLarge 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...
متن کاملAsymptotics of the Gauss Hypergeometric Function with Large Parameters, I
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...
متن کاملMultidimensional Fractional Calculus Operators Involving the Gauss Hypergeometric Function
This paper deals with some multidimensional integral operators involving the Gauss hypergeometric function in the kernel and generating the multidimensional modified fractional calculus operators introduced in [8]. Some mapping properties, weighted inequalities, a formula of integration by parts and index laws are obtained.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Computational Mathematics
سال: 2012
ISSN: 1019-7168,1572-9044
DOI: 10.1007/s10444-012-9283-y