In this paper we investigate the representation of integrals involving product Legendre Chi function, polylogarithm function and log function. We will show that in many cases these take an explicit form Riemann zeta Dirichlet Eta lambda other special functions. Some examples illustrating theorems be detailed.

This paper describes a numerical implementation in Maple V R. 5 of an algorithm to compute the Legendre–Fenchel conjugate, namely the Linear-time Legendre Transform algorithm. After a brief motivation on the importance of the Legendre–Fenchel transform, we illustrate the information the conjugate gives (how to test for convexity or compacity, and how to smooth a convex function), with several e...

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...

Legendre expansion of the ν ¯ ν ⇀ ↽ e + e − kernel: Influence of high order terms. Abstract We calculate the Legendre expansion of the rate of the process ν + ¯ ν ↔ e + + e − up to 3 rd order extending previous results of other authors which only consider the 0 th and 1 st order terms. Using different closure relations for the moment equations of the radiative transfer equation we discuss the p...

Abstract. It was shown by P. J. Davis that the Newton-Cotes quadrature formula is convergent if the integrand is an analytic function that is regular in a sufficiently large region of the complex plane containing the interval of integration. In the present paper, a bound on the error of the Newton-Cotes quadrature formula for analytic functions is derived. Also the bounds on the Legendre polyno...

this paper presents an exact analytical solution for two-dimensional conductive heat transfer in spherical composite pressure vessels .the vessels are in spherical shape and fibers are winded in circumferential direction. the analytical solution is obtained under the general boundary conditions which consist of convection, conduction and radiation inside/outside of vessel. the heat transfer equ...