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Calling Sequence
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product(f,k)
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product(f,k=m..n)
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product(f,k=alpha)
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product(f,k=expr)
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Product(f,k)
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Product(f,k=m..n)
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Product(f,k=alpha)
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Product(f,k=expr)
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Parameters
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f
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expression
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k
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name, the product index
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m, n
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integers or arbitrary expressions
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alpha
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RootOf
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expr
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expression not containing k
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Description
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The product command is for computing symbolic products. It is used to compute a formula for an indefinite or definite product. If a formula cannot be computed, Maple returns the product unevaluated. A typical example would be product(x+k, k=0..n-1) which returns the formula GAMMA(x+n)/GAMMA(x). If you want to multiply a finite sequence of values, rather than compute a formula, use the mul command. For example mul(x+k, k=0..2) returns x*(x+1)*(x+2). Although the product command can be used to compute explicit products, the mul command should be used in programs for explicit products.
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You can enter the product command using either the 1-D or 2-D calling sequence. For example, product(x+k, k=0..n-1) is equivalent to .
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The call product(f, k) computes the indefinite product of f(k) with respect to k. That is, it computes a formula g such that g(k+1)/g(k) = f(k) for all k.
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The call product(f, k = m..n) computes the definite product of f(k) over the given range m..n, that is, it computes f(m) f(m+1) ... f(n). The definite product is equivalent to g(n+1)/g(m) where g is the indefinite product. For example, product(n,n) = product(k, k=1..n-1) = GAMMA(n).
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If m = n+1 then the value returned is 1. If m > n+1 then 1/product(f, k=n+1..m-1) is the value returned.
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The call product(f, k= alpha) computes the definite product of f(k) over the roots of a polynomial where alpha must be a RootOf.
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The call product(f, k= expr) substitutes the value of expr for k in f.
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If Maple cannot find a closed form for the product, the function call itself is returned. (The prettyprinter displays the product function using a stylized product sign.)
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The capitalized function name Product is the inert product function, which simply returns unevaluated. It appears gray so that it is easily distinguished from a returned product calling sequence.
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Examples
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>
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For a finite sequence of values, use the mul command.
>
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>
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>
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>
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>
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>
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Compatibility
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The product command was updated in Maple 2016; see Advanced Math.
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