𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Some monotonicity properties of polynomials with equally spaced zeros

✍ Scribed by L. Lorch

Publisher
Akadmiai Kiad
Year
1976
Tongue
English
Weight
433 KB
Volume
27
Category
Article
ISSN
1588-2632

No coin nor oath required. For personal study only.

πŸ“œ SIMILAR VOLUMES

Monotonicity Properties of the Zeros of
Monotonicity Properties of the Zeros of Ultraspherical Polynomials
✍ ÁrpΓ‘d Elbert; Panayiotis D. Siafarikas πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 111 KB

## Let x (*) n, k , k=1, 2, ..., [nΓ‚2], denote the k th positive zero in increasing order of the ultraspherical polynomial P (\*) n (x). We prove that the function [\*+(2n 2 +1)Γ‚ (4n+2)] 1Γ‚2 x (\*) n, k increases as \* increases for \*> &1Γ‚2. The proof is based on two integrals involved with the s