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We consider the associated linear problem for a q-analogue of the fifthPainleve equation (qPV). We identify a lattice of connection preservingdeformations in the space of the connection data for the linear problem withthe lattice of translational Backlund transformations for qPV, hence, show alltranslational Backlund transformations possess a Lax pair. We shall show thatthe big q-Laguerre polynomials, and a suitable generalization, solve a specialcase of the linear problem, hence, find solutions to qPV in terms ofdeterminants of Hankel matrices with entries consisting of rational orhypergeometric functions.

A study of the associated linear problem for $q$-$\mathrm{P}_{\mathrm{V}}$