Ladder operator relations for hypergeometric functions

Abstract

Two first-order differential operators are introduced to generate recursion formulae for hypergeometric functions. These operators, on the one hand, factorise the associated second-order operator and, on the other hand, reproduce the equations resulting from the action of the supersymmetry generators on the positive-energy solution of the Coulomb field. The results for the confluent hypergeometric functions also provide a natural basis for constructing ladder operator recursion relations for the Coulomb Green function with the outgoing wave boundary condition.