IBM 5100

60
Dyadic (Two-Argument) Form: Binomial A!B
The binomial function result is the number of different combinations of argumenf B
that can be taken A at a time. The result of A! 8 is also the (A+l) th coefficient of
the binomial expansion of the 8
th
power. The arguments can be numeric scalars,
vectors, or other arrays. The argument must be the same shape, unless one of the
arguments is a scalar or any single-element array. Arguments of the same shape
have the same shape result:
2 !l+
f.)
2!6
w
y
Z ! ........ J-----Argument B
x
1 1::'
.,J
~5 ! ()
0
() ! :3
1
The combinations of
>- .. ....------
argument 8 taken
2!3
argument A(2) at a time
3
If one argument is a scalar or a single-element array, the shape of the result is the
same as that of the other argument. The single element is applied to every element
of the multielement array:
1
1
~5
'+
o 1
2 3
3
I.>
:I.
10
0
:L
'')
':N
~5 ! ~5
1
0
:I,
")
.:-
3
I+! 1+
1+ :I,
B~"2 2~)0 1 2 3
B
2 ! "',+ ~5
10 10 7,87~:j I.)
10
4, I ~5 1+
If noninteger arguments are used, this function relates to the beta function as
follows: Beta (P,Q) is equal to 7Qx(P-l)! P+Q-l