Geodesic
On the Monotonic Variation of the Zeros of Ultraspherical Polynomials with the Parameters
Canadian mathematical bulletin, Tome 27 (1984) no. 4, pp. 472-477

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DOI

We show that increases with λ, for 0< λ < 1, being the kth zero of the ultraspherical polynomial and f(λ) a suitable function of λ. As a consequence, some inequalities for and an estimate for can be obtained.
DOI : 10.4153/CMB-1984-074-1
Mots-clés : 33A45, 34A50, zeros of ultraspherical polynomials, Sturm comparison theorem 
Spigler, Renato. On the Monotonic Variation of the Zeros of Ultraspherical Polynomials with the Parameters. Canadian mathematical bulletin, Tome 27 (1984) no. 4, pp. 472-477. doi: 10.4153/CMB-1984-074-1
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     title = {On the {Monotonic} {Variation} of the {Zeros} of {Ultraspherical} {Polynomials} with the {Parameters}},
     journal = {Canadian mathematical bulletin},
     pages = {472--477},
     year = {1984},
     volume = {27},
     number = {4},
     doi = {10.4153/CMB-1984-074-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-074-1/}
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