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--- author(s): M2Fest2005 DE
doc ///
Key
binomial
(binomial, Number, Number)
(binomial, RingElement, ZZ)
(binomial, ZZ, ZZ)
Headline
binomial coefficient
Usage
binomial(n,k)
Inputs
n:{ZZ,RingElement}
k:ZZ -- must be non-negative
Outputs
:Number
the binomial coefficient, the coefficient of @TEX "$x^k$"@ in
@TEX "$(1+x)^n$"@ or @TEX "$n(n-1)...(n-k+1)/k!$"@.
Description
Example
binomial(13,6)
binomial(-1,3)
Text
When either @TT "n"@ or @TT "k"@ are not @TO ZZ@ objects, the
@TO Gamma@ function is used, i.e., @TEX "$\\binom{n}{k} =
\\frac{\\Gamma(n + 1)}{\\Gamma(k + 1)\\Gamma(n - k + 1)}$"@.
Example
binomial(7.5, pi)
Text
A polynomial may also be used for @TT "n"@.
Example
R = QQ[x]
binomial(x + 3, 3)
///
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