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Product (Product)

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Product[f, {i, imax}]
evaluates the product f.
Product[f, {i, imin, imax}]
starts with i=imin.
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 ... f.
Product[f, i]
gives the indefinite product .
  • Product[f, {i, imax}] can be entered as f.
  • Product[f, {i, imin, imax}] can be entered as f.
  • The limits should be underscripts and overscripts of Product 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 i gives f.
  • 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.
EXAMPLESCLOSE ALL
Basic Examples   (5)
Numeric product:
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Symbolic product:
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Use Esc prod Esc to enter Product and Ctrl+_ to enter the lower limit, then Ctrl+% for the upper limit:
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Infinite product:
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Multiple product with product over m performed first:
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