Hypergeometric-type differential equations: second kind solutions and related integrals

摘要

A Rodrigues-type representation for the second kind solutions of a second-order differential equation of hypergeometric type is given. This representation contains some integrals related with relevant special functions. For these integrals, a general recurrence relation, which only involves the coefficients of the differential equation, is also presented. Finally, an extension of the Rodrigues type representation for the second solution of a second-order difference equation of hypergeometric type is indicated.