I. Theoretical Analysis
Gamma Function is defined in the following,
Using integration by parts, one sees that:
From the above calculation，and note that
If is a positive integer, one can obtain:
If it meets a condition , obviously given that,
Calculate quadratic ,
Using integration by polar coordinates, , and,
then, one sees that
II. Numerical analysis
Evaluate Gamma function in matlab.
1.Evaluate the gamma function with a scalar and a vector.
>> y = gamma(0.5) y = 1.7725 >> y = gamma(-pi:pi) y = 1.0157 -3.1909 6.8336 -7.8012 1.1046 0.9482 1.7621
2.Plot the gamma function and its inverse.
% PlotGammaFunctionExample.m fplot(@gamma) hold on fplot(@(x) 1./gamma(x)) legend('\Gamma(x)','1/\Gamma(x)') hold off grid on
In addition, the domain of the gamma function extends to negative real numbers by analytic continuation, with simple poles at the negative integers. This extension arises from repeated application of the recursion relation
More information see here.
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