|L||A difference operator|
Returns if has no hypergeometric solution over , or such that any solution of is also a solution of .
hyper returns only the solutions that are hypergeometric over , i.e. the solutions such that . It does not return any eventual solution that is hypergeometric over but not over . In addition, hyper does not attempt to return several linearly independent hypergeometric solutions, so if it finds one, there could be some others.
has hypergeometric solutions:
1 --> L := (n-1)*E^2 - (n^2+3*n-2)*E + 2*n*(n+1); 2 --> tex(hyper(L));
This shows that is a solution, but there are others: we can verify that divides on the right, which proves that is another hypergeometric solution:
3 --> R := E - n - 1; 4 --> Q := L / R; 5 --> tex(L - Q*R);