I would like to derive the correct Laguerre function from the differential equation but the differential equations seems different from the original one.
What is the correct differential equation and other kinds of equations under the hypergeometric family?
Maple output Kummer, i am not familiar with mathematica, can mathematica do?
The goal is to make target1 and target2 equal
s := x; tau := alpha - 1 - x; source := s*Diff(y(x),x$2)+tau*Diff(y(x),x)+n*y(x)=0; sol := dsolve(source,y(x)); target1 :=ztrans(sol,x,z); target2 := sqrt(1-a^2)/(1-a/z)*((1/z-a)/(1-a/z))^(N-1);