gamma¶
-
sherpa.utils.
gamma
(z)[source] [edit on github]¶ Calculate the Gamma function.
- Parameters
z (scalar or array) – -171 <= z <- 171.6
- Returns
val – The gamma function of the input.
- Return type
scalar or array
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.
Examples
>>> gamma(2.3) 1.1667119051981603
>>> gamma([2.3,1.9]) array([ 1.16671191, 0.96176583])