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### hyper

Usage

hyper L

Parameter Type Description
L A difference operator

Returns

Returns if 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 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);


Next: kernel Up: Supported functions Previous: factor   Contents   Index
Manuel Bronstein 2002-09-04