  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.
