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Description
Essentially, this stuff
sage: binomial(10, 0.1)
1
What I would have expected it to give as output is
sage: gamma(10+1)/gamma(10-0.1+1)/gamma(0.1+1)
1.32919082253922
This enhancement has to be done on the sage side since both mpir and pari don't give the correct answer. Using the gamma function in these special cases will also take care of complex numbers.
But, we must avoid changing the whole implementation to the gamma function - that was also giving incorrect results and was fixed in #12448. The sage.rings.arith.binomial function itself is a bit of a mess and it is hard to figure out what will eventually get executed in that code.
Component: basic arithmetic
Keywords: binomial
Issue created by migration from https://trac.sagemath.org/ticket/14897