Abstract
Polynomialsp 1,(z),p 2 (z), of degreen are defined by the relation\(p_1 (z) + p_2 (z)\prod\nolimits_{i = 1}^3 {(z - b_l )^{v_1 } } = O(z^{ - n - 1} ),z \to \infty \), where\(\sum\nolimits_{i = 1}^3 {v_i = 0} \). We obtain the asymptotic behavior of these polynomials asn→∞ and show that it agrees with a previous conjecture.
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Communicated by Edward B. Saff.
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Nuttall, J. Asymptotics of generalized jacobi polynomials. Constr. Approx 2, 59–77 (1986). https://doi.org/10.1007/BF01893417
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DOI: https://doi.org/10.1007/BF01893417