# 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.

# Details

• The Casoratian determinant is defined as: Det[Table[DiscreteShift[yi,{n,j}],{i,m},{j,0,m-1}]].
• If the sequences y1,y2, are linearly dependent, the Casoratian vanishes everywhere.

# Examples

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## 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 :

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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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