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AHELP for CIAO 4.11 Sherpa v1

# igamc

Context: utilities

## Synopsis

Calculate the complement of the regularized incomplete Gamma function (upper)

## Syntax

`igamc(a,x)`

## Description

Calculate the CEPHES function, igamc, in the range [a > 0; x > 0].

The function, igamc, is defined by

```igamc(a,x) = 1 - igam(a,x)

= 1/gamma(a) Int_(x)^(Inf) e^(-t) t^(a-1) dt
```

where "igam" represents the regularized incomplete Gamma function (see "ahelp igam"), and "gamma(a)" the complete Gamma function. (If the igam and igamc functions are *not* regularized, then their sum is not one, but is the complete Gamma function, gamma(a).)

In this implementation, both arguments must be positive. The integral is evaluated by either a power series or continued fraction expansion, depending on the relative values of a and x. Arguments can be in scalar or array form.

### Accuracy

Tested at random a, x.

#### a x Relative error:

arithmetic domain domain # trials peak rms
IEEE 0.5,100 0,100 200000 1.9e-14 1.7e-15
IEEE 0.01,0.5 0,100 200000 1.4e-13 1.6e-15

### Reference

Cephes Math Library Release 2.0: April, 1987. Copyright 1985, 1987 by Stephen L. Moshier. Direct inquiries to 30 Frost Street, Cambridge, MA 02140.

## Examples

### Example 1

`sherpa> igamc(1,2)`

Calculate igamc with a=1, x=2.

### Example 2

`sherpa> igamc([1,2],[2,3])`

Calculate igamc with a=[1,2], x=[2,3] .

## Bugs

See the bugs pages on the Sherpa website for an up-to-date listing of known bugs.

## See Also

tools
aprates, modelflux
utilities
calc_chisqr, calc_energy_flux, calc_model_sum, calc_photon_flux, calc_source_sum, calc_stat, gamma, igam, incbet, lgam