Wolfram Language & System 10.3 (2015)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE 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.

DetailsDetails

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

ExamplesExamplesopen allclose all

Basic Examples  (4)Basic Examples  (4)

These sequences are linearly independent:

 Out[1]=
 Out[2]=

The following sequences are linearly dependent:

 Out[1]=
 Out[2]=

Here the sequences are linearly dependent only when :

 Out[1]=

The Casoratian for a linear equation:

 Out[1]=

Except for a constant, the result is the same as for the explicit solution:

 Out[2]=
 Out[3]=