DifferenceDelta

DifferenceDelta[f,i]

gives the discrete difference .

DifferenceDelta[f,{i,n}]

gives the multiple difference .

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 Options

  • DifferenceDelta[f,i] can be input as if. The character is entered diffd 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 i,jf. The character \[InvisibleComma], entered as ,, can be used instead of the ordinary comma.
  • DifferenceDelta[f,{i,n,h}] can be input as { i,n,h }f.
  • DifferenceDelta[f,,Assumptions->assum] uses the assumptions assum in the course of computing discrete differences.

Examples

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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 diffd, and subscripts using :

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DifferenceDelta is the inverse operator to Sum:

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Scope  (21)

Applications  (9)

Properties & Relations  (7)

Neat Examples  (1)

See Also

Sum  DiscreteShift  DiscreteRatio  DifferenceQuotient  RSolve  FactorialPower  D  ReplaceAll  Differences

Introduced in 2008
(7.0)