Mathematica > Mathematics and Algorithms > Calculus > Product ()
BUILT-IN MATHEMATICA SYMBOL

Product

Product[f, {i, imax}]
evaluates the product .

Product[f, {i, imin, imax}]
starts with .

Product[f, {i, imin, imax, di}]
uses steps di.

Product[f, {i, {i1, i2, ...}}]
uses successive values , , ... .

Product[f, {i, imin, imax}, {j, jmin, jmax}, ...]
evaluates the multiple product .

Product[f, i]
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 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.
  • 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:

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Symbolic product:

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

In[1]:=
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Out[1]=

Infinite product:

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Out[1]=

Multiple product with product over performed first:

In[1]:=
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Out[1]=

Scope (25)Scope (25)

Options (3)Options (3)

Applications (6)Applications (6)

Properties & Relations (4)Properties & Relations (4)

Possible Issues (2)Possible Issues (2)

Neat Examples (1)Neat Examples (1)

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