Asymptotic Monotonicity of the Relative Extrema of Jacobi Polynomials
1994 ◽
Vol 46
(06)
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pp. 1318-1337
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Keyword(s):
Abstract If μk,n (α,β) denotes the relative extrema of the Jacobi polynomial P(α,β) n(x), ordered so that μ k+1,n (α,β) lies to the left of μ k,n (α,β), then R. A. Askey has conjectured twenty years ago that for for k = 1,…, n — 1 and n = 1,2,=. In this paper, we give an asymptotic expansion for μ k,n (α,β) when k is fixed and n → ∞, which corrects an earlier result of R. Cooper (1950). Furthermore, we show that Askey's conjecture is true at least in the asymptotic sense.
1953 ◽
Vol 5
◽
pp. 301-305
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Keyword(s):
1970 ◽
Vol 22
(3)
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pp. 582-593
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1968 ◽
Vol 16
(2)
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pp. 101-108
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Keyword(s):
1969 ◽
Vol 66
(1)
◽
pp. 105-107
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1985 ◽
Vol 37
(5)
◽
pp. 979-1007
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1971 ◽
Vol 70
(2)
◽
pp. 243-255
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1968 ◽
Vol 64
(3)
◽
pp. 687-690
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1968 ◽
Vol 64
(3)
◽
pp. 695-698
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Keyword(s):
1985 ◽
Vol 37
(3)
◽
pp. 551-576
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1967 ◽
Vol 63
(2)
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pp. 457-459
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