Some extremal properties of the integral of Legendre polynomials are given, which are of independent interest. Meanwhile they show that a conjecture of P. Erdős[1] is plausible and maybe provides some means to prove this conjecture.
机构:
E China Normal Univ, Dept Math, Shanghai Key Lab PMMP, Shanghai 200241, Peoples R ChinaE China Normal Univ, Dept Math, Shanghai Key Lab PMMP, Shanghai 200241, Peoples R China