Confluent Equation Research Articles

Confluence of fuchsian second-order differential equations

Ordinary linear homogeneous second-order differential equations with polynomial coefficients including one in front of the second derivative are studied. Fundamental definitions for these equations: of s-rank of the singularity (different from Poincare rank), of s-multisymbol of the equation, and of s-homotopic transformations are proposed. The generalization of Fuchs' theorem for confluent Fuchsian equations is proved. The tree structure of types of equations is shown, and the generalized confluence theorem is proved.

The Schrodinger equation for the interaction potential x2+λx2/(1+gx2) and the first Heun confluent equation

The authors present systematically the solutions and the quasi-polynomial solutions for the Schrodinger equation with the x2+ lambda x2/(1+gx2) interaction potential with the help of the first Heun confluent equation or spheroidal Heun equation.