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Congruences concerning Legendre polynomials II
Legendre polynomial congruence character sum binary quadratic form
2011/2/22
Let p > 3 be a prime, and let m be an integer with p ∤ m. In the paper we solve some conjectures of Z.W.
Let p > 3 be a prime, and let m be an integer with p ∤ m. In the paper we solve some conjectures of Z.W. Sun concerning Pp−1 k=0 (6k)! mk(3k)!k!3 (mod p), and show that for integers m, n w...
Let p be an odd prime. In the paper, by using the properties of Legendre polynomials we prove some congruences for P p−1 2 k=0 2k k 2 m−k (mod p2). In particular, we confirm se...
On the Inequality of P. Turan for Legendre Polynomials
Orthogonal polynomials Legendre polynomials Turan Inequality Positivity
2008/6/27
On the Inequality of P. Turan for Legendre Polynomials.
SOME EXTREMAL PROPERTIES OF THE INTEGRAL OF LEGENDRE POLYNOMIALS
Lagrange interpolation Legend
2007/12/11
Some extremal properties of the integral of Legendre polynomials are given, which are of independent interest. Meanwhile they show that a conjecture of P. Erdos[1] is plausible and maybe provides some...