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 OptionsDetails and Options

  • DiscreteShift[f, i] can be input as . The character is entered using EscshiftEsc 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 . The character \[InvisibleComma], entered as Esc,Esc, can be used instead of the ordinary comma.
  • DiscreteShift[f, {i, n, h}] can be input as .
  • DiscreteShift[f, ..., Assumptions->assum] uses the assumptions assum in the course of computing discrete shifts.

ExamplesExamplesopen allclose all

Basic Examples (4)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 EscshiftEsc, and subscripts using Ctrl+_:

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The shift with respect to i of scoped operators:

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