Usage
hyper L
Parameter | Type | Description |
---|---|---|
L |
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A difference operator |
Returns
Returnsif
has no hypergeometric solution over
, or
such that any solution of
is also a solution of
.
Remarks
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.
Example
The equation
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 thatis 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);