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Casoratian

Casoratian[{y1, y2, ...}, n]
gives the Casoratian determinant for the sequences y1, y2, ... depending on n.
Casoratian[eqn, y, n]
gives the Casoratian determinant for the basis of the solutions of the linear difference equation eqn involving y[n+m].
Casoratian[eqns, {y1, y2, ...}, n]
gives the Casoratian determinant for the system of linear difference equations eqns.
  • Linear independence of the functions y1, y2, ... is equivalent to the vanishing of the Casoratian.
EXAMPLESCLOSE ALL
Basic Examples   (4)
These sequences are linearly independent:
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The following sequences are linearly dependent:
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Here the sequences are linearly dependent only when a=0:
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The Casoratian for a linear equation:
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Except for a constant, the result is the same as for the explicit solution:
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