Some notes on the roots of ultraspherical polynomials
โ Scribed by G.I. Natanson; V.V. Glagovskii
- Publisher
- Elsevier Science
- Year
- 1970
- Weight
- 304 KB
- Volume
- 10
- Category
- Article
- ISSN
- 0041-5553
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
## Let x (*) n, k , k=1, 2, ..., [nร2], denote the k th positive zero in increasing order of the ultraspherical polynomial P (\*) n (x). We prove that the function [\*+(2n 2 +1)ร (4n+2)] 1ร2 x (\*) n, k increases as \* increases for \*> &1ร2. The proof is based on two integrals involved with the s
It is proved that the chromatic polynomial of a connected graph with n vertices and m edges has a root with modulus at least (m&1)ร(n&2); this bound is best possible for trees and 2-trees (only). It is also proved that the chromatic polynomial of a graph with few triangles that is not a forest has a