NOTE ON THE DEFINITE INTEGRAL OVER PRODUCTS OF THREE 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

SOLVING NONLINEAR TWO-DIMENSIONAL VOLTERRA INTEGRAL EQUATIONS OF THE FIRST-KIND USING BIVARIATE SHIFTED LEGENDRE FUNCTIONS

In this paper, a method for finding an approximate solution of a class of two-dimensional nonlinear Volterra integral equations of the first-kind is proposed. This problem is transformedto a nonlinear two-dimensional Volterra integral equation of the second-kind. The properties ofthe bivariate shifted Legendre functions are presented. The operational matrices of integrationtogether with the produ...

histological evaluation of the effect of three medicaments; trichloracetic acid, formocresol and mineral trioxide aggregate on pulpotomized teeth of dogs

چکیده ندارد.