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Product

  • Product[ f , i , imax ] evaluates the product .
  • Product[ f , i , imin , imax ] starts with i = imin. Product[ f , i , imin , imax , di ] uses steps di.
  • Product[ f , i , imin , imax , j , jmin , jmax , ... ] evaluates the multiple product .
  • Product[ f , i , imax ] can be entered as .
  • can be entered as prod or \[Product].
  • Product[ f , i , imin , imax ] can be entered as .
  • The limits should be underscripts and overscripts of in normal input, and subscripts and superscripts when embedded in other text.
  • Product evaluates its arguments in a non-standard way (see Section A.4.2).
  • Product uses the standard Mathematica iteration specification.
  • The iteration variable i is treated as local.
  • 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.
  • Product is output in StandardForm using .
  • See the Mathematica book: Section 1.5.4.
  • See also Implementation NotesA.9.55.15MainBookLinkOldButtonDataA.9.55.15.
  • See also: Do, Sum, Table, NProduct.

    Further Examples

    A symbolic product.

    In[1]:=

    Out[1]=

    This product tends to (slowly) as tends to infinity.

    In[2]:=

    Out[2]=

    In[3]:=

    Out[3]=

    In[4]:=