Incomplete gamma function
Y = gammainc(X,A)
Y = gammainc(X,A,tail)
Y = gammainc(X,A,'scaledlower')
Y = gammainc(X,A,'scaledupper')
The incomplete gamma function is
where is the gamma function, gamma(a).
Note: The syntax gammainc(X,A) is equivalent to the function P(A,X) defined above, where X is the limit of integration in each case.
For any A ≥ 0, gammainc(X,A) approaches 1 as X approaches infinity. For small X and A, gammainc(X,A) is approximately equal to X^A, so gammainc(0,0) = 1.
Y = gammainc(X,A) returns the incomplete gamma function of corresponding elements of X and A. The elements of A must be nonnegative. Furthermore, X and A must be real and the same size (or either can be scalar).
Y = gammainc(X,A,tail) specifies the tail of the incomplete gamma function. The choices for tail are 'lower' (the default) and 'upper'. The upper incomplete gamma function is defined as:
When the upper tail value is close to 0, the 'upper' option provides a way to compute that value more accurately than by subtracting the lower tail value from 1.
Y = gammainc(X,A,'scaledlower') and Y = gammainc(X,A,'scaledupper') return the incomplete gamma function, scaled by
These functions are unbounded above, but are useful for values of X and A where gammainc(X,A,'lower') or gammainc(X,A,'upper') underflow to zero.
 Cody, J., An Overview of Software Development for Special Functions, Lecture Notes in Mathematics, 506, Numerical Analysis Dundee, G. A. Watson (ed.), Springer Verlag, Berlin, 1976.
 Abramowitz, M. and I.A. Stegun, Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series #55, Dover Publications, 1965, sec. 6.5.