An Integral Equation Involving Legendre Functions

Legendre-type integrands and convex integral functions

In this paper, we study the properties of integral functionals induced on LE(S, μ) by closed convex functions on a Euclidean space E. We give sufficient conditions for such integral functions to be strongly rotund (well-posed). We show that in this generality functions such as the Boltzmann-Shannon entropy and the Fermi-Dirac entropy are strongly rotund. We also study convergence in measure and...

On Parameter Differentiation for Integral Representations of Associated Legendre Functions

For integral representations of associated Legendre functions in terms of modified Bessel functions, we establish justification for differentiation under the integral sign with respect to parameters. With this justification, derivatives for associated Legendre functions of the first and second kind with respect to the degree are evaluated at odd-halfinteger degrees, for general complex-orders, ...

The Study of Triple Integral Equations with Generalized Legendre Functions

On the numerical solution of Urysohn integral equation using Legendre approximation

Urysohn integral equation is one of the most applicable topics in both pure and applied mathematics. The main objective of this paper is to solve the Urysohn type Fredholm integral equation. To do this, we approximate the solution of the problem by substituting a suitable truncated series of the well known Legendre polynomials instead of the known function. After discretization of the problem o...

Numerical solution of nonlinear integral equations by Galerkin methods with hybrid Legendre and Block-Pulse functions

In this paper, we use a combination of Legendre and Block-Pulse functionson the interval [0; 1] to solve the nonlinear integral equation of the second kind.The nonlinear part of the integral equation is approximated by Hybrid Legen-dre Block-Pulse functions, and the nonlinear integral equation is reduced to asystem of nonlinear equations. We give some numerical examples. To showapplicability of...