Asymptotic Properties of Zeros of Hypergeometric Polynomials
β Scribed by Peter L Duren; Bertrand J Guillou
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 181 KB
- Volume
- 111
- Category
- Article
- ISSN
- 0021-9045
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The zeros of the Meixner polynomial m n (x; ;, c) are real, distinct, and lie in (0, ). Let : n, s denote the s th zero of m n (n:; ;, c), counted from the right; and let :Γ n, s denote the sth zero of m n (n:; ;, c), counted from the left. For each fixed s, asymptotic formulas are obtained for both
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## 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