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Inequalities for ultraspherical polynomials. Proof of a conjecture of I. Raşa

✍ Scribed by Nikolov, Geno

Book ID
124141897
Publisher
Elsevier Science
Year
2014
Tongue
English
Weight
243 KB
Volume
418
Category
Article
ISSN
0022-247X

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📜 SIMILAR VOLUMES

On a Conjecture Concerning Monotonicity
On a Conjecture Concerning Monotonicity of Zeros of Ultraspherical Polynomials
✍ Dimitar K. Dimitrov 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 235 KB

Let C \* n , n=0, 1, ..., \*>&1Â2 be the ultraspherical (Gegenbauer) polynomials, orthogonal on (&1, 1) with respect to the weight (1&x 2 ) \*&1Â2 . Denote by `n, k (\*), k=1, ..., [nÂ2] the positive zeros of C \* n enumerated in decreasing order. The problem of finding the ``extremal'' function f f

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✍ F.M. Dong 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 138 KB

Let P(G, \*) denote the chromatic polynomial of a graph G. It is proved in this paper that for every connected graph G of order n and real number \* n, (\*&2) n&1 P(G, \*)&\*(\*&1) n&2 P(G, \*&1) 0. By this result, the following conjecture proposed by Bartels and Welsh is proved: P(G, n)(P(G, n&1))