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Zeros of Jacobi polynomials P/sub n//sup (. cap alpha. /sub n/,. beta. /sub n/)/(x)

Journal Article · · Trans. Am. Math. Soc.; (United States)
DOI:https://doi.org/10.2307/1998916· OSTI ID:6898370
If r/sub n/ and s/sub n/ denote, respectively, the smallest and largest zeros of the Jacobi polynomial P/sub n//sup (..cap alpha../sub n/,..beta../sub n/)/, where ..cap alpha../sub n/ > 1, ..beta../sub n/ - 1, and if lim/sub n ..-->.. infinity/ ..cap alpha../sub n//(2n + ..cap alpha../sub n/ + ..beta../sub n/ + 1) = ..cap alpha.. and if lim/sub n ..-->.. infinity/ ..beta../sub n//(2n+..cap alpha../sub n/ + ..beta../sub n/ + 1) = b, then the numbers r/sub a,b/ and s/sub a,b/ are determined. Furthermore, the zeros of )P/sub n//sup (..cap alpha../sub n/,..beta../sub n/)(x))/sub n = 0//sup infinity/ are dense in (r/sub a,b/, s/sub a,b/).
DOE Contract Number:
EY-76-S-02-2075
OSTI ID:
6898370
Journal Information:
Trans. Am. Math. Soc.; (United States), Journal Name: Trans. Am. Math. Soc.; (United States) Vol. 249:1; ISSN TAMTA
Country of Publication:
United States
Language:
English