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:
Saratov NG Chernyshevskii State Univ, Dept Mech & Math, Saratov 410060, RussiaSaratov NG Chernyshevskii State Univ, Dept Mech & Math, Saratov 410060, Russia