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AHELP for CIAO 4.16 Sherpa

# lgam

Context: utilities

## Synopsis

Calculate the log (base e) of the Gamma function.

## Syntax

```lgam(z)

z - scalar or array```

## Examples

### Example 1

```>>> lgam(104.56)
380.21387239435785```

### Example 2

```>>> lgam([104.56,2823.4])
array([   380.21387239,  19607.42734396])```

### PARAMETERS

The parameter for this function is:

Parameter Definition
z 0 <= z <= 2.556348e305

### Return value

The return value from this function is:

val -- The log of the Gamma function of the input.

### Notes

This implementation is provided by the Cephes Math Library [1] . For arguments greater than 13, the logarithm of the Gamma function is approximated by the logarithmic version of Stirling's formula using a polynomial approximation of degree 4. Arguments between -33 and +33 are reduced by recurrence to the interval [2,3] of a rational approximation. The cosecant reflection formula is employed for arguments less than -33.

Relative errors are

domain # trials peak rms
0,3 28000 5.4e-16 1.1e-16
2.718,2.556e305 40000 3.5e-16 8.3e-17

The error criterion was relative when the function magnitude was greater than one but absolute when it was less than one.

The following test used the relative error criterion, though at certain points the relative error could be much higher than indicated.

domain # trials peak rms
-200,-4 10000 4.8e-16 1.3e-16

### References

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

## Bugs

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

tools::response
color_color, modelflux
tools::statistics
aprates
utilities
calc_chisqr, calc_energy_flux, calc_model_sum, calc_photon_flux, calc_source_sum, calc_stat, gamma, igam, igamc, incbet