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binomial

compute binomial coefficients

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

binomial(n, r)

nr

Parameters

n, r

-

expressions

Description

• 

The binomial(n,r) function computes binomial coefficients.

• 

You can enter the command binomial using either the 1-D or 2-D calling sequence. For example, binomial(n, 2) is equivalent to n2 .

• 

If the arguments are both non-negative integers with 0rn, then binomialn,r=n!r!nr!, which is the number of distinct sets of r objects that can be chosen from n distinct objects.

• 

If n and r are integers that do not satisfy 0rn, or n and r are rationals or floating-point numbers, then the general definition is used, that is,

nr=Γn+1Γr+1Γnr+1

• 

At all points n,r where none of n, r, and nr is a negative integer, the above definition is equivalent to:

nr=limt0Γn+t+1Γr+1Γn+tr+1

  

In the case that n is a negative integer, binomial(n,r) is defined by this limit. If r is a negative integer, by the symmetry relation binomial(n,r) = binomial(n,n-r), the above limit is used.

  

In the case that exactly two of the expressions n, r, and nr are negative integers, Maple also signals the invalid_operation numeric event, allowing the user to control this singular behavior by catching the event. See numeric_events for more information.

• 

For symbolic arguments, some simplifications, for example, binomial(n, 1) = n, can be made, but typically binomial returns unevaluated.

Examples

binomial4,2

6

(1)

binomial2,12

163π

(2)

binomial2.1,2+3I

56.5616761998.27156511I

(3)

binomialn,2

binomialn,2

(4)

expand

12n212n

(5)

NumericStatusinvalid_operation=false:

binomial3,5

21

(6)

NumericStatusinvalid_operation

true

(7)

See Also

combinat

combinat[multinomial]

combinat[numbcomb]

expand

GAMMA

initialfunctions

numeric_events

NumericStatus

 


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