gamma¶

sherpa.utils.gamma(z)¶

Calculate the Gamma function.

Parameters:	z (scalar or array) – -171 <= z <- 171.6
Returns:	val
Return type:	scalar or array

See also

lgam(): The log of the Gamma function.
igam(): The incomplete Gamma function.

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])