Mathematica 9 is now available
THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION.
Wolfram Mathematica Documentation Center
DOCUMENTATION CENTER SEARCH
New to Mathematica? Find your learning path »
Mathematica > Mathematics and Algorithms > Calculus > Discrete Calculus > DiscreteShift >
Mathematica > Mathematics and Algorithms > Discrete Mathematics > Discrete Calculus > DiscreteShift >
BUILT-IN MATHEMATICA SYMBOLSee Also »|More About »

DiscreteShift

DiscreteShift
gives the discrete shift .
DiscreteShift
gives the multiple shift .
DiscreteShift
gives the multiple shift of step h.
DiscreteShift
computes partial shifts with respect to i, j, ....
MORE INFORMATION
  • All quantities that do not explicitly depend on the variables given are taken to have constant partial shift.
EXAMPLESCLOSE ALL
Basic Examples   (4)
Shift with respect to i:
Shift with step h:
Multiple shifts with respect to i:
Enter using Esc shift Esc, and subscripts using Ctrl+_:
The shift with respect to i of scoped operators:
Shift with respect to i:
In[1]:=
Click for copyable input
Out[1]=
Shift with step h:
In[2]:=
Click for copyable input
Out[2]=
 
Multiple shifts with respect to i:
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
 
Enter using Esc shift Esc, and subscripts using Ctrl+_:
In[1]:=
Click for copyable input
Out[1]=
 
The shift with respect to i of scoped operators:
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
In[3]:=
Click for copyable input
Out[3]=
Scope   (10)
Compute the first and second shift:
First and second shift with step h:
The first partial shifts with respect to i and j :
Higher partial shifts:
Partial shifts with steps r and s:
Elementary functions:
Integer functions:
Holonomic sequences satisfy a linear difference equation:
Sums:
Shifting inside the summation sign:
In this case i is not a free variable:
Products:
Differencing product limits:
Integrals:
Shifting integration limits:
Limits:
Here the i is not a free variable:
Applications   (2)
Define a symbolic mean operator using DiscreteShift:
It also works with scoping constructs:
Use on special functions:
Use DiscreteShift to define derivatives:
Properties & Relations   (3)
DiscreteShift is a linear operator:
Product rule:
Quotient rule:
Chain rule:
DiscreteShift can be expressed in terms of DifferenceDelta:
DifferenceDelta can be expressed in terms of DiscreteShift:
DiscreteRatio can be expressed in terms of DiscreteShift:
Possible Issues   (1)
Using ReplaceAll to implement DiscreteShift can be dangerous:
DiscreteShift understands scoping rules:
New in 7
Ask a question about this page  |  Suggest an improvement  |  Leave a message for the team
Format:   HTML  |  CDF