In mathematics, Turán's inequalities are some inequalities for Legendre polynomials found by Pál Turán (and first published by ). There are many generalizations to other polynomials, often called Turán's inequalities, given by 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
See also Askey–Gasper inequality Sturm's theorem
References