• Integral Inequalities for Self-Reciprocal Polynomials

    • Fulltext


        Click here to view fulltext PDF

      Permanent link:

    • Keywords


      Self-reciprocal polynomials; integral inequalities.

    • Abstract


      Let $n\geq 1$ be an integer and let $\mathcal{P}_n$ be the class of polynomials 𝑃 of degree at most 𝑛 satisfying $z^nP(1/z)=P(z)$ for all $z\in C$. Moreover, let 𝑟 be an integer with $1\leq r\leq n$. Then we have for all $P\in\mathcal{P}_n$:


      with the best possible factors

      \begin{equation*}\alpha_n(r)=\begin{cases}\prod^{r-1}_{j=0}\left(\frac{n}{2}-j\right)^2, < \text{if 𝑛 is even},\\ \frac{1}{2}\left[\prod^{r-1}_{j=0}\left(\frac{n+1}{2}-j\right)^2+\prod^{r-1}_{j=0}\left(\frac{n-1}{2}-j\right)^2\right], < \text{if 𝑛 is odd},\end{cases}\end{equation*}



      This refines and extends a result due to Aziz and Zargar (1997).

    • Author Affiliations


      Horst Alzer1

      1. Morsbacher Str. 10, D-51545 Waldbröl, Germany
    • Dates

  • Proceedings – Mathematical Sciences | News

    • Editorial Note on Continuous Article Publication

      Posted on July 25, 2019

      Click here for Editorial Note on CAP Mode

© 2022-2023 Indian Academy of Sciences, Bengaluru.