[Rd] choose incorrect for fractional and some negative integer values (PR#10766)

Jerry.Lewis at biogenidec.com Jerry.Lewis at biogenidec.com
Fri Feb 15 22:45:03 CET 2008

Full_Name: Jerry W. Lewis
Version: 2.6.2
OS: Windows XP Professional
Submission from: (NULL) (

choose() returns incorrect values for all fractional arguments, regardless of
sign.  It returns 0 when both arguments are negative integers, which is not
always correct (as in some formulations of the negative hypergeometric).

Examples (correct answers from Maple's binomial function):

choose( 4.75,2.75)  # should be 8.90625
choose(-0.75,-0.5)  # should be 1.6692536833481464
choose(-1.75,-0.5)  # should be 0.55641789444938212
choose(-2.75,-1.5)  # should be 0.15897654127125204
choose(-5,   -7)    # should be 15

The correct answers for first two can be verified easily since choose(n,k)
should equal
but does not for fractional arguments.  The latter three are instances where
beta incorrectly returns NaN, as noted in PR#10763

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