Turán's inequalities
In mathematics, Turán's inequalities are some inequalities for Legendre polynomials found by Pál Turán (1950) (and first published by Szegö (1948)). There are many generalizations to other polynomials, often called Turán's inequalities, given by (E. F. Beckenbach, W. Seidel & Otto Szász 1951) and other authors.
If is the th Legendre polynomial, Turán's inequalities state that
For , the th Hermite polynomial, Turán's inequalities are
whilst for Chebyshev polynomials they are