text: In atmospheric radiation, Chandrasekhars X- and Y-function appears as the solutions of problems involving diffusive reflection and transmission, introduced by the Indian American astrophysicist Subrahmanyan Chandrasekhar. The Chandrasekhars X- and Y-function 
  where the characteristic function  is an even polynomial in  generally satisfying the condition
  and  is the optical thickness of the atmosphere. If the equality is satisfied in the above condition, it is called conservative case, otherwise non-conservative. These functions are related to Chandrasekhar's H-function as
  and also