Wolfram Language & System 10.4 (2016)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.View current documentation (Version 11.2)


evaluates the product .

starts with .

uses steps di.

uses successive values , , .

evaluates the multiple product .

gives the indefinite product .

Details and OptionsDetails and Options

  • Product[f,{i,imax}] can be entered as .
  • can be entered as EscprodEsc 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 uses the standard Wolfram Language 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.
  • The indefinite product is defined so that the ratio of terms with successive gives .
  • Definite and indefinite summation can be mixed in any order.
  • For sums, the following options can be given:
  • Assumptions$Assumptionsassumptions to make about parameters
    GenerateConditionsFalsewhether to generate answers that involve conditions on parameters
    MethodAutomaticmethod to use
    RegularizationNonewhat regularization to use
    VerifyConvergenceTruewhether to verify convergence
  • Possible values for Regularization include: None and . specifies different schemes for different variables in a multiple product.
  • Product can do essentially all products that are given in standard books of tables.
  • Product is output in StandardForm using .

ExamplesExamplesopen allclose all

Basic Examples  (5)Basic Examples  (5)

Numeric product:

Click for copyable input

Symbolic product:

Click for copyable input

Use EscprodEsc to enter and Ctrl+_ to enter the lower limit, then Ctrl+% for the upper limit:

Click for copyable input

Infinite product:

Click for copyable input

Multiple product with product over performed first:

Click for copyable input
Introduced in 1988
| Updated in 2008