# 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 \$Assumptions assumptions to make about parameters GenerateConditions False whether to generate answers that involve conditions on parameters Method Automatic method to use Regularization None what regularization to use VerifyConvergence True whether 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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