The hypergeometric function of a real variable is computed for arbitrary real parameters. The transformation theory of the hypergeometric function is used to obtain rapidly convergent power series. The divergences that occur in the individual terms of the transformation for integer parameters are re
The early history of the hypergeometric function
β Scribed by Jacques Dutka
- Publisher
- Springer-Verlag
- Year
- 1984
- Tongue
- English
- Weight
- 893 KB
- Volume
- 31
- Category
- Article
- ISSN
- 0003-9519
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract An asymptotic representation is obtained for the hypergeometric function ${\bf F}(a+\lambda,bβ\lambda,c,1/2β1/2z)$\nopagenumbers\end as $|\lambda|\rightarrow\infty$\nopagenumbers\end with $|{\rm ph}\,\lambda|<\pi$\nopagenumbers\end. It is uniformly valid in the __z__βplane cut in an app
This paper deals with the study of the hypergeometric function with matrix arguments F(A,B;C;z). Conditions for matrices A, B, C so that the series representation of the hypergeometric function be convergent for Jz I = 1 and satisfies a matrix differential equation are given. After the study of beta