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 i1, i2, .

Product[f,{i,imin,imax},{j,jmin,jmax},]

evaluates the multiple product .

Product[f,i]

gives the indefinite product .

Details and Options

  • Product[f,{i,imax}] can be entered as f.
  • can be entered as prod or \[Product].
  • 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 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 "Dirichlet". {reg1,reg2,} 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 .

Examples

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Basic Examples  (5)

Numeric product:

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Symbolic product:

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Use prod to enter and to enter the lower limit, then for the upper limit:

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Infinite product:

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Multiple product with product over performed first:

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Scope  (28)

Options  (4)

Applications  (6)

Properties & Relations  (4)

Possible Issues  (2)

Neat Examples  (2)

See Also

Do  Sum  Table  NProduct  RSolve  Times  DiscreteRatio  ParallelProduct

Tutorials

Introduced in 1988
(1.0)
| Updated in 2008
(7.0)