Generalized Wavelet Transform Associated with Legendre Polynomials

Fractional differential equations with Legendre polynomials

On the generalized Legendre transform and monopole metrics

In the generalized Legendre transform construction the Kähler potential is related to a particular function. Here, the form of this function appropriate to the k-monopole metric is calculated from the known twistor theory of monopoles.

On Polar Legendre Polynomials

We introduce a new class of polynomials {Pn}, that we call polar Legendre polynomials, they appear as solutions of an inverse Gauss problem of equilibrium position of a field of forces with n + 1 unit masses. We study algebraic, differential and asymptotic properties of this class of polynomials, that are simultaneously orthogonal with respect to a differential operator and a discrete-continuou...

Congruences concerning Legendre Polynomials

Let p be an odd prime. In the paper, by using the properties of Legendre polynomials we prove some congruences for È p−1 2 k=0 2k k ¡ 2 m −k (mod p 2). In particular, we confirm several conjectures of Z.W. Sun. We also pose 13 conjectures on supercongruences.

Legendre polynomials and supercongruences

Let p > 3 be a prime, and let Rp be the set of rational numbers whose denominator is not divisible by p. Let {Pn(x)} be the Legendre polynomials. In this paper we mainly show that for m,n, t ∈ Rp with m 6≡ 0 (mod p), P[ p 6 ](t) ≡ − (3 p ) p−1 ∑ x=0 (x3 − 3x + 2t p ) (mod p)