Incomplete gamma function
Y = gammainc(X,A)
Y = gammainc(X,A,tail)
Y = gammainc(X,A,'scaledlower')
Y
= gammainc(X,A,'scaledupper')
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:
$$\text{gammainc}\left(\text{x,a,'upper'}\right)=\frac{1}{\Gamma (a)}{\displaystyle \underset{x}{\overset{\infty}{\int}}{t}^{a-1}{e}^{-t}dt}$$
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
$$\Gamma (a+1)\left(\frac{{e}^{x}}{{x}^{a}}\right).$$
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.
Note:
When |
[1] 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.
[2] Abramowitz, M. and I.A. Stegun, Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series #55, Dover Publications, 1965, sec. 6.5.
gamma
| gammaincinv
| gammaln
| psi