Case of the two difference equations

Enter the command ``pasrec():''. You will be asked to enter the left member of the first equation, the order of this equation ($${M}$$ here), then a recurrent step ($\alpha$ here) associated to this equation. Likewise, you will be asked to enter the left member of the second equation, the order of this equation ($${N}$$ here), then a recurrent step ($\beta$ here) associated to this equation. Eventually, you will be asked to give the expression of the unknown function (here, $${f(z)}$$) then to enter an accuracy that will be used in the computations. Watch out ! You have to add ``;'' or ``:'' to all the answers that you give to the program. In case of oversight, the program will ask you again the same question which you must answer by ``;'' or ``:''. The program answers you a basis of entire functions candidate. Then, you may run again the program asking for a better accuracy (i.e. entering an accuracy constant smaller) in order to see if the solution remains unchanged or, in the contrary, if there are functions that appear or disappear.