dojox.math.factorial incorrectly returning NaN for non-integers

[Douglas Hays]

dojox.math.factorial(1.5) returns NaN but should return
sqrt(pi)*3/4 ~= 1.329340388179137 as defined by the gamma function.
You can also verify this with the Windows calc.exe program (scientific view has the n! button).

[Eugene Lazutkin]

Try not to overdo it: one can always complain that it doesn't work for negative and complex numbers, quaternions, and octonions too --- there are generalizations for these and other cases. ;-)

It reminds me of my robotics prof, who asked us to write a solver for a trivial quadratic polynomial, and embarrassed students by pointing out that their solution doesn't work for complex numbers, doesn't show that there are no solutions (a == 0, b == 0, c != 0), doesn't detect degenerated linear cases (a == 0, b != 0, or a != 0, b == 0), and in some cases any values are valid solutions (a == 0, b == 0, c == 0).

[Douglas Hays]

reimplement factorial via gamma function

[Douglas Hays]

(In [20977]) Fixes #10374. Implement _gamma function so that fractional factorial can be calculated consistent with windows calc.exe program and TI calculators, but optimized for integers since this is the normal case. Add automated testcases.