DifferenceDelta

DifferenceDelta[f,i]
gives the discrete difference .

DifferenceDelta[f,{i,n}]
gives the multiple difference TemplateBox[{f, i, n}, DifferenceDelta3].

DifferenceDelta[f,{i,n,h}]
gives the multiple difference with step h.

DifferenceDelta[f,i,j,]
computes the partial difference with respect to i, j, .

Details and OptionsDetails and Options

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

ExamplesExamplesopen allclose all

Basic Examples  (4)Basic Examples  (4)

Difference with respect to i:

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Difference with step h:

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The fifth difference with respect to i:

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The second difference with respect to i and step h:

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Enter using EscdiffdEsc, and subscripts using Ctrl+_:

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DifferenceDelta is the inverse operator to Sum:

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Introduced in 2008
(7.0)