We find an exact expression for the unique positive solution of a discrete Painlevé equation that arises in the context of static membranes, and as an example of a quantum minimal surface considered by Arnlind, Hoppe and Kontsevich. It transpires that this is generated by a special combination of Backlund transformations for Painlevé V, admitting a sequence of classical solutions which we are able to express explicitly using Wronskians of modified Bessel functions. Extensions to other quantum curves and higher order discrete Painleve equations will briefly be mentioned, as well as the connection with very recent results by Felder and Hoppe which relate these solutions to orthogonal polynomials                                                                                                          
 
 
 
 
 
 
 
 
 

https://indico.math.cnrs.fr/event/14895/