DiscreteShift

DiscreteShift[f,i]

gives the discrete shift TemplateBox[{{f, (, i, )}, i}, DiscreteShift2]=f(i+1).

DiscreteShift[f,{i,n}]

gives the multiple shift .

DiscreteShift[f,{i,n,h}]

gives the multiple shift of step h.

DiscreteShift[f,i,j,]

computes partial shifts with respect to i, j, .

Details and Options

  • DiscreteShift[f,i] can be input as if. The character is entered using shift or \[DiscreteShift]. The variable i is entered as a subscript.
  • All quantities that do not explicitly depend on the variables given are taken to have constant partial shift.
  • DiscreteShift[f,i,j] can be input as i,jf. The character \[InvisibleComma], entered as ,, can be used instead of the ordinary comma.
  • DiscreteShift[f,{i,n,h}] can be input as {i,n,h}f.
  • DiscreteShift[f,,Assumptions->assum] uses the assumptions assum in the course of computing discrete shifts.

Examples

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Basic Examples  (4)

Shift with respect to i:

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Shift with step h:

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Multiple shifts with respect to i:

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Enter using shift, and subscripts using :

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The shift with respect to i of scoped operators:

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Scope  (10)

Applications  (2)

Properties & Relations  (3)

Possible Issues  (1)

See Also

DifferenceDelta  DiscreteRatio  DifferenceQuotient  RSolve  GeneratingFunction  ReplaceAll

Introduced in 2008
(7.0)