Year: 2026
Type: preprint
Abstract: Let $P=P_n^{(α,β)}$ be the $n$-th degree Jacobi polynomial, which is orthogonal in $[-1,1]$ with respect to the weight function $(1-x)^α(1+x)^β$, $α,β>-1$. For parameters $(α,β)$ satisfying either $α\geqβ\geq 1/2$ or $α\geq 1/2$, $β=-1/2$, we prove the inequality $$ P(1)-P(x)\geq P^{\prime}(x)\,(1-x),\quad x\in [0,1], $$ which may be viewed as a complement to Finite Increment Theorem for Jacobi polynomials.
Source: arXiv (Cornell University)
Author: Nikolov, Geno
Institution: Sofia University "St. Kliment Ohridski"
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7165930809
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