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Inverse incomplete gamma function

`x = gammaincinv(y,a)`

x = gammaincinv(y,a,tail)

`x = gammaincinv(y,a)`

evaluates the inverse
incomplete gamma function for corresponding elements of `y`

and `a`

,
such that` y = gammainc(x,a)`

. The elements of `y`

must
be in the closed interval `[0,1]`

, and those of `a`

must
be nonnegative. `y`

and `a`

must
be real and the same size (or either can be a scalar).

`x = gammaincinv(y,a,tail)`

specifies the
tail of the incomplete gamma function. Choices are `'lower'`

(the
default) to use the integral from 0 to `x`

, or `'upper'`

to
use the integral from `x`

to infinity.

These two choices are related as:

`gammaincinv(y,a,'upper') = gammaincinv(1-y,a,'lower')`

.

When `y`

is close to 0, the `'upper'`

option
provides a way to compute `x`

more accurately than
by subtracting `y`

from 1.

[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.