Synopsis
Calculate the Gamma function.
Syntax
gamma(z) z - scalar or array
Examples
Example 1
>>> gamma(2.3) 1.1667119051981603
Example 2
>>> gamma([2.3,1.9]) array([ 1.16671191, 0.96176583])
PARAMETERS
The parameter for this function is:
| Parameter | Definition |
|---|---|
| z | -171 <= z <- 171.6 |
Return value
The return value from this function is:
val -- The gamma function of the input.
Notes
This implementation is provided by the Cephes Math Library [1] . Arguments |x| >= 34 are reduced by recurrence and the function approximated by a rational function of degree 6/7 in the interval (2,3). Large arguments are handled by Stirling's formula. Large negative arguments are made positive using a reflection formula.
Relative errors are
| domain | # trials | peak | rms |
|---|---|---|---|
| -170,33 | 20000 | 2.3e-15 | 3.3e-16 |
| -33,33 | 20000 | 9.4e-16 | 2.2e-16 |
| 33,171.6 | 20000 | 2.3e-15 | 3.2e-16 |
Errors for arguments outside the test range will be larger owing to amplification by the exponential function.
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.
See Also
- 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, igam, igamc, incbet, lgam