Hypergeometric type q-difference equations: Rodrigues type representation for the second kind solution

摘要

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