A Functional Equation in the Theory of Fluids

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Abstract
Two functional equations of the form ψ2(s) − E(s)φ2(s) = V(s), where s is a complex variable and E(s) and V(s) are given even polynomials, are solved for the even entire functions ψ and φ which are required to behave like cosh[αs + o(s)] for large |Rls|. Two cases are considered: (i) V of degree zero and E of degree two and (ii) V of degree eight and E of degree six. In the second case the polynomials must satisfy a condition in order for ψ and φ to have the right asymptotic behavior. These functional equations arise in solving the Percus‐Yevick equation for a mixture of hard spheres with nonadditive diameters.