IJPAM: Volume 41, No. 5 (2007)

INEQUALITIES FOR THE JACOBI POLYNOMIALS
AND THEIR DERIVATIVES

Abedallah Rababah
Department of Mathematics and Statistics
Faculty of Science and Arts
Jordan University of Science and Technology
P.O. Box 3030, Irbid, 22110, JORDAN
e-mail: rababah@just.edu.jo


Abstract.Some inequalities for the Jacobi polynomials and their derivatives are presented in this paper. An upper bound is also given for rational terms containing the Jacobi polynomials and the first derivative $P_n^{(\alpha , \beta)'}(x)$, $\alpha , \beta > -1$ at the roots $x_{kn}=\cos(\theta_{kn})$, $k=1,2, \ldots,n$ of the Jacobi polynomial $P_n^{(\alpha,\beta)} (x)$.

Received: August 6, 2007

AMS Subject Classification: 41A05, 41A10

Key Words and Phrases: orthogonal polynomials, Jacobi polynomials

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 41
Issue: 5