This is documentation for Mathematica 6, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)

Product ()

Updated In 6 Graphic
Product[f, {i, imax}]
evaluates the product f.
Product[f, {i, imin, imax}]
starts with i=imin.
Product[f, {i, imin, imax, di}]
uses steps di.
Product[expr, {i, {i1, i2, ...}}]
uses successive values i1, i2, ....
Product[f, {i, imin, imax}, {j, jmin, jmax}, ...]
evaluates the multiple product ... f.
  • Product[f, {i, imax}] can be entered as f.
  • Product[f, {i, imin, imax}] can be entered as f.
  • The limits should be underscripts and overscripts of in normal input, and subscripts and superscripts when embedded in other text.
  • Product uses the standard Mathematica iteration specification.
  • The iteration variable i is treated as local, effectively using Block.
  • If the range of a product is finite, i is typically assigned a sequence of values, with f being evaluated for each one.
  • In multiple products, the range of the outermost variable is given first.
  • The limits of a product need not be numbers. They can be Infinity or symbolic expressions.
  • If a product cannot be carried out explicitly by multiplying a finite number of terms, Product will attempt to find a symbolic result. In this case, f is first evaluated symbolically.
  • Product can do essentially all products that are given in standard books of tables.
Numeric product:
In[1]:=
Click for copyable input
Out[1]=
 
Symbolic product:
In[1]:=
Click for copyable input
Out[1]=
 
Use Esc prod Esc to enter and Ctrl+Space to enter lower limit, then Ctrl+% for the upper limit:
In[1]:=
Click for copyable input
Out[1]=
 
Infinite product:
In[1]:=
Click for copyable input
Out[1]=
 
Multiple product with product over m performed first:
In[1]:=
Click for copyable input
Out[1]=
New in 1 | Last modified in 6