## 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
Computing the Hypergeometric Function
β Scribed by Robert C. Forrey
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 318 KB
- Volume
- 137
- Category
- Article
- ISSN
- 0021-9991
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β¦ Synopsis
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 removed using a finite difference technique.
π SIMILAR VOLUMES
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By showing certain combinations of the Gaussian hypergeometric functions Ε½ c . Ε½ d . Ε½ . F a, b; a q b; 1 y x and F a y β¦, b q β¦; a q b; 1 y x to be monotone on 0, 1 Ε½ . for given a, b, c, d g 0, Ο± , a F b, and cd, the authors study the problem of Γ Ε½ . Ε½ c . comparing these two functions. They find