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admits continuous American Mathematical Society asymptotic form becomes infinite Bessel function boundary condition llb bounded function class h completes the proof complex parameter constant satisfying continuous first partial continuous partial derivatives denote derivatives and satisfies derivatives with respect double integral equa equation 11a equation 55 equation 68 equivalent erential equation following theorem form 31 Furthermore given equation given in connection Green's function Green's identity hypothesis integral equation 23 integrand integro-differential equation interchanged Langer last term left hand member lemma member of 32 member of 99 member of equation non-homogeneous integro-differential obtained by differentiation order of integration partial differential equation point x,y properties relation is uniformly remains finite replaced restricted right hand member right member satisfies the equality satisfies the relations satisfy the inequality satisfying the condition second partial derivatives sign of integration solution of equation system l7 tinuous tion Transformation uniformly bounded uniformly convergent variables write the equation written