Some Useful Collective Properties of Bessel, Marcum Q-Functions and Laguerre Polynomials

Special functions have been used widely in many problems of applied sciences. However, there are considerable numbers of problems in which exact solutions could not be achieved because of undefined sums or integrals involving special functions. These handicaps force researchers to seek new properties of special functions. Many problems that could not be solved so far would be solved by means of these efforts. Therefore in this article, we derived some useful properties and interrelations of each others of Bessel functions, Marcum Q-functions and Laguerre polynomials

T-N method for the critical thickness of one-speed neutrons in a slab with forward and backward scattering

WOS: 000245403100004The critical slab problem in the case of combination of forward and backward scattering with usual isotropic scattering is studied for one-speed neutrons in a uniform finite slab by using TN method based on Chebyshev polynomial approximation and Marshak boundary conditions. It is shown that TN method gives accurate results in one-dimensional geometry and is very efficient both in derivation of equations and rapid convergence. Numerical results obtained by TN method are compared against the PN method in tabular form, which agreed quite well. (c) 2006 Elsevier Ltd. All rights reserved