Function choose

Binomial coefficient. Equivalent to R's choose(). Takes single numbers.

n may be any real number. k is rounded to the nearest integer (as R does, which also warns when k is not close to an integer); choose(n, k) is 0 for k < 0 and 1 for k = 0. For integer n the result is an integer (exact up to 2^53).

Edge cases where R differs from the mathematical value, followed by default (rCompatible: false returns the mathematical value instead):

• n within 1e-9 max(1, |n|) of an integer is treated as that integer, so choose(1e-10, 2) is 0 (mathematically -5e-11); for n < 0 and k >= 30 the tolerance is relative to k - 1 - n;
• choose(n, Infinity) is 0 for n >= 0 (otherwise NaN);
• choose(±Infinity, k) is NaN for k >= 30 (±Infinity below).