BUILT-IN MATHEMATICA SYMBOL

Casoratian

Casoratian[{y₁, y₂, ...}, n]
gives the Casoratian determinant for the sequences , , ... depending on n.

Casoratian[eqn, y, n]
gives the Casoratian determinant for the basis of the solutions of the linear difference equation eqn involving .

Casoratian[eqns, {y₁, y₂, ...}, n]
gives the Casoratian determinant for the system of linear difference equations eqns.

Details Details

The Casoratian determinant is defined as: Det[Table[DiscreteShift[y_i, {n, j}], {i, m}, {j, 0, m-1}]].
Linear independence of the functions , , ... is equivalent to the vanishing of the Casoratian.

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 :

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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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