binom(n,k), REAL n and k with non negative elements. If both are non- scalars, they must have the same dimensions |

binom(n,k), where n >= 0 and k >= 0 are REAL scalars with n >= k returns a binomial coefficient. n and k need not be integers, but when they are binom(n,k) returns n!/(k!*(n-k)!) as an exact integer. Otherwise it returns gamma(n+1)/(gamma(k+1)*gamma(n-k+1)), where gamma(x) is the Gamma function. When just one of n and k is a scalar, binom(n,k) returns a REAL vector, matrix or array consisting of binomial coefficients computed from the scalar and each of the elements of the other argument. When neither n or k is a scalar, both must have exactly the same dimensions and the result is an array with the same dimesions consisting of of binomial coefficients computed from corresponding elements of n and k. Examples: Cmd> binom(4,run(0,4)) # vector(binom(4,0),...,binom(4,4)) (1) 1 4 6 4 1 Cmd> binom(run(3,7),3) # vector(binom(3,3),...,binom(7,3)) (1) 1 4 10 20 35 Cmd> binom(run(3,7),run(0,4)) # vector(binom(3,0),...,binom(7,4)) (1) 1 4 10 20 35 See also lgamma().

Gary Oehlert 2003-01-15