DiscreteShift
![TemplateBox[{{f, (, i, )}, i}, DiscreteShift2]=f(i+1)](Files/DiscreteShift.zh/25.png "TemplateBox[{{f, (, i, )}, i}, DiscreteShift2]=f(i+1)"){kind=small}
DiscreteShift
DiscreteShift[f,i]
给出离散移位 ![TemplateBox[{{f, (, i, )}, i}, DiscreteShift2]=f(i+1)](Files/DiscreteShift.zh/1.png "TemplateBox[{{f, (, i, )}, i}, DiscreteShift2]=f(i+1)"){kind=small}
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DiscreteShift[f,{i,n}]
给出多重移位 
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DiscreteShift[f,{i,n,h}]
给出步长 h 的多重移位.
DiscreteShift[f,i,j,…]
给出关于 i, j, … 的部分移位.
更多信息和选项
- DiscreteShift[f,i] 可以输入 if.字符 通过输入
shift
或 \[DiscreteShift]得到. 变量 i 作为下标输入. - 所有没有明确依赖于给定变量的数据量采用常量的部分移位.
- DiscreteShift[f,i,j] 可以输入为 i,jf.字符 \[InvisibleComma]，通过
,
输入， 可以代替普通的逗号. - DiscreteShift[f,{i,n,h}] 可以输入为 {i,n,h}f.
- DiscreteShift[f,…,Assumptions->assum] 在计算离散移位中用假定 assum.
范例
打开所有单元 关闭所有单元基本范例 (4)
DiscreteShift[f[i], i]DiscreteShift[f[i], {i, h}]DiscreteShift[Sin[i ^ 3 2Pi / 7], {i, 10}]DiscreteShift[Fibonacci[i], {i, 5}]
输入 
输入下标：Subscript[, {i, 5}]i!DiscreteShift[Sum[f[k], {k, i + a, i + b}], i]DiscreteShift[Limit[f[x], x -> i], i]DiscreteShift[Derivative[i][f][x], i]范围 (10)
基本用法 (3)
DiscreteShift[f[i], i]DiscreteShift[f[i], {i, 2}]DiscreteShift[f[i], {i, 1, h}]DiscreteShift[f[i], {i, 2, h}]
Subscript[, i, j]f[i, j]Subscript[, {i, 2}, j]f[i, j]Subscript[, {i, 1, r}, {j, 1, s}]f[i, j]特殊序列 (3)
DiscreteShift[2 ^ i, i]DiscreteShift[i ^ 4 + 20 * i ^ 2 + 11i ^ 3, {i, 3}]DiscreteShift[(i ^ 2 + 5) / (i - 7), i]DiscreteShift[Floor[i], i]DiscreteShift[FractionalPart[i], i]DiscreteShift[Round[i], {i, 3}]DiscreteShift[Fibonacci[i], {i, 5}]DiscreteShift[Gamma[i], {i, 3}]DiscreteShift[CatalanNumber[i], {i, 3}]DiscreteShift[BesselJ[i, x], {i, 2}]特殊运算 (4)
DiscreteShift[Sum[f[i], i], i]DiscreteShift[Sum[f[i], {i, n, n + a}], n]DiscreteShift[Sum[f[i, j], i], j]DiscreteShift[Sum[f[i], {i, a, b}], i]DiscreteShift[Product[f[i], i], i]DiscreteShift[Product[f[i, j], i], j]DiscreteShift[Product[f[i], {i, m, n}], m]DiscreteShift[Product[f[i], {i, m, n}], n]DiscreteShift[Integrate[f[i], i], i]DiscreteShift[Integrate[f[i, j], i], j]DiscreteShift[Integrate[f[i], {i, a, j}], j]DiscreteShift[Limit[f[i], i -> j], j]DiscreteShift[Limit[f[i], i -> j], i]应用 (2)
用 DiscreteShift 定义一个符号均值运算：
DiscreteMean[f_, i_] := Simplify[(1/2)(Subscript[, i]f + f)]DiscreteMean[f[i], i]DiscreteMean[Sum[f[i], i], i]DiscreteMean[Limit[f[i], i -> j], i]DiscreteMean[Gamma[i], i]用 DiscreteShift 定义导数：
Der[f_, i_] := Limit[(DiscreteShift[f, {i, 1, h}] - f) / h, h -> 0]Der[i ^ 2, i]Der[Sin[i], i]Der[E ^ i, i]属性和关系 (3)
DiscreteShift 是一个线性运算：
Subscript[, i](a f[i] + b g[i])Subscript[, i](f[i]g[i])Subscript[, i](f[i]/g[i])Subscript[, i]f[g[i]]DiscreteShift 可以按 DifferenceDelta 表示：
DiscreteShiftDelta[f_, {i_, n_}] := Underoverscript[∑, k = 0, n]Binomial[n, k]Subscript[, {i, k}]fDiscreteShiftDelta[f[i], {i, 2}]DiscreteShift[f[i], {i, 2}]Simplify[%% - %]DifferenceDelta 可以按 DiscreteShift 表示：
DifferenceDeltaShift[f_, {i_, n_}] := Underoverscript[∑, k = 0, n]Binomial[n, k](-1)^n - kSubscript[, {i, k}]fDifferenceDeltaShift[f[i], {i, 2}]DifferenceDelta[f[i], {i, 2}]DiscreteRatio 可以按 DiscreteShift 表示：
DiscreteShift[f[i], i] / f[i]DiscreteRatio[f[i], i]可能存在的问题 (1)
用 ReplaceAll 执行 DiscreteShift 可能无效：
Integrate[f[x], x] /. x -> x + 1
DiscreteShift 中可以应用范围规则：
DiscreteShift[Integrate[f[x], x], x]
Wolfram Research (2008)，DiscreteShift，Wolfram 语言函数，https://reference.wolfram.com/language/ref/DiscreteShift.html.
文本
Wolfram Research (2008)，DiscreteShift，Wolfram 语言函数，https://reference.wolfram.com/language/ref/DiscreteShift.html.
CMS
Wolfram 语言. 2008. "DiscreteShift." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/ref/DiscreteShift.html.
APA
Wolfram 语言. (2008). DiscreteShift. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/DiscreteShift.html 年