Definition of Product Symbol

Prerequisites

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Description

The definition of the product symbol is the product of a sequence of factors. \(\htmlId{tooltip-var}{x}_{\htmlId{tooltip-iter}{i}}\) is multiplied by all the consecutive terms to get the final result.

Equation

\[\htmlId{tooltip-product}{\prod}_{\htmlId{tooltip-const}{a} = \htmlId{tooltip-iter}{i}}^{\htmlId{tooltip-2const}{b}} \htmlId{tooltip-var}{x}_{\htmlId{tooltip-iter}{i}} = \htmlId{tooltip-const}{a}_{\htmlId{tooltip-iter}{i}} \htmlId{tooltip-const}{a}_{\htmlId{tooltip-iter}{i} + 1} ... \htmlId{tooltip-const}{a}_{\htmlId{tooltip-2const}{b}}, \htmlId{tooltip-const}{a} < \htmlId{tooltip-2const}{b}\]

Symbols Used

\(x\)

This is a symbol for any generic variable. It can hold any value, whether that be an integer or a real number, or a complex number, or a matrix etc.

\(i\)

This is the symbol for an iterator, a variable that changes value to refer to a sequence of elements.

\(b\)

This is a symbol for any secondary generic constant. It can hold any numerical value

\(\prod\)

This is the product symbol in mathematics, denoted as the uppercase Greek letter Pi. It is used to indicate the product of a sequence of factors.

\(a\)

This is a symbol for any generic constant. It can hold any numerical value

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