What is the symbol for the continuous product in mathematics?

In summary, the discrete summation is represented by ##\sum## and the continuous by ##\int##. The discrete product is symbolized by ##\prod## and the continuous product, also known as the product integral, can be represented by ##\int\!\!\!\!\!\times##, ##\int\!\!\!\!_P##, or ##\int\!\!\!\!\!\Pi## depending on the context. Alternatively, the regular discrete product symbol ##\Pi## can also be used.
  • #1
Jhenrique
685
4
If the discrete summation is symbolized by ##\sum## and the continuous by ##\int##, so, by analogoy, the discrete product is symbolized by ##\prod## and you already thought what is the symbol for the continuous product?
 
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  • #2
It's called a "product integral" and has symbol:

##\prodi## ... drat PFLatex may not have one!

Looks like: ##\int\!\!\!\!\!\times## or ##\int\!\!\!\!_P## though I figure a cap-pi would work too ... since the sum-integral symbol is ##\int\!\!\!\!\! _\Sigma## ... the display mode would look like:
$$\int\!\!\!\!\!\!\times\; ,\qquad \int\!\!\!\!\!\! P\; ,\qquad \int\!\!\!\!\!\! \Pi$$


... or a tall, elongated, but lower-case letter "pi".

Usually acceptable to just use the regular discrete product ##\Pi## since the context can make the meaning clear.
 
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What is a symbol of continuous product?

A symbol of continuous product is a mathematical notation used to represent the multiplication of a series of numbers or variables without explicitly writing out each term. It is denoted by the capital Greek letter "pi" (∏).

What does the symbol of continuous product mean?

The symbol of continuous product represents the product of a sequence of terms, similar to how the symbol of summation (Σ) represents the sum of a sequence of terms.

How is the symbol of continuous product used in mathematics?

The symbol of continuous product is commonly used in areas of mathematics such as calculus, algebra, and number theory to represent the product of a series of numbers or variables. It is also used in various formulas and equations to simplify calculations.

What are the properties of the symbol of continuous product?

The symbol of continuous product has similar properties to the symbol of summation, such as the associative and distributive properties. It also has the property that if any term in the sequence is equal to 0, the entire product will be equal to 0.

Can the symbol of continuous product be used for infinite sequences?

Yes, the symbol of continuous product can be used for infinite sequences. In this case, it represents an infinite product, which can be evaluated using techniques such as limits and convergence tests.

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