On the Extreme Zeros of Jacobi Polynomials
نویسندگان
چکیده
By applying the Euler–Rayleigh method to a specific representation of Jacobi polynomials as hypergeometric functions, we obtain new bounds for their largest zeros. In particular, derive upper and lower bound $$1-x_{nn}^2(\lambda )$$ , with $$x_{nn}(\lambda being zero n-th ultraspherical polynomial $$P_n^{(\lambda )}$$ . For every fixed $$\lambda >-1/2$$ limit ratio our does not exceed 1.6. This paper is continuation [16].
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ژورنال
عنوان ژورنال: Lecture Notes in Computer Science
سال: 2023
ISSN: ['1611-3349', '0302-9743']
DOI: https://doi.org/10.1007/978-3-031-32412-3_22