Application of Wiener-Hopf technique to linear non homogenous integral equations for a new representation of Chandrasekhar's H-function in radiative transfer, its existence and uniqueness

In this paper the linear non linear non homogenous integral equations of H- functions is considered to find a new form of H- function as its solution.The Wiener Hopf technique is used to express a known function into two functions with different zones of analyticity.The linear non homogenous integral equation is thereafter expressed into two different sets of function having different zones of regularity.The modified form of Lioville's theorem is used thereafter.Cauchy's integrl formulae are used to determine functional representation over the cut region in a complex plane.The new form off H function is derived both for conservative and non conservative cases.The exiatence of solution of linear nonhomogenous integral equations and its uniqueness are shown.For numerical calculation of this new H-function,a set of useful formulae are derived both for conservative and non conservative cases.