Abstract
Inequalities recently conjectured for all zeros of Jacobi polynomials \(P_n^{(\alpha,\beta)}\) of all degrees n are modified and conjectured to hold (in reverse direction) in considerably larger domains of the (α,β)-plane.
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Gatteschi, L.: On the zeros of Jacobi polynomials and Bessel functions. In: International Conference on Special Functions: Theory and Computation (Turin, 1984). Rend. Semin. Mat. Univ. Politec. Torino (special issue) 1985, 149–177 (1985)
Gautschi, W.: On a conjectured inequality for the largest zero of Jacobi polynomials. Numer. Algorithms (2008, in press)
Gautschi, W.: On conjectured inequalities for zeros of Jacobi polynomials. Numer. Algorithms (2008, in press)
Gautschi, W., Giordano, C.: Luigi Gatteschi’s work on aymptotics of special functions and their zeros. Numer. Algorithms (2008, in press)
Gautschi, W., Leopardi, P.: Conjectured inequalities for Jacobi polynomials and their largest zeros. Numer. Algorithms 45(1–4), 217–230 (2007)
Szegö, G.: Orthogonal Polynomials, 4th edn., vol. 23. American Mathematical Society, Colloquium Publications. American Mathematical Society, Providence (1975)
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Gautschi, W. New conjectured inequalities for zeros of Jacobi polynomials. Numer Algor 50, 293–296 (2009). https://doi.org/10.1007/s11075-008-9230-7
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DOI: https://doi.org/10.1007/s11075-008-9230-7