# gamma approximation : what is module cmath and where is it located ?

Thu Jul 30 00:24:11 EDT 2009

```The following numerical approximation for Euler's Gamma function
is found in http://en.wikipedia.org/wiki/Lanczos_approximation

from cmath import *

# Coefficients used by the GNU Scientific Library
g = 7
p = [0.99999999999980993, 676.5203681218851, -1259.1392167224028,
771.32342877765313, -176.61502916214059, 12.507343278686905,
-0.13857109526572012, 9.9843695780195716e-6, 1.5056327351493116e-7]

def gamma(z):
z = complex(z)
# Reflection formula
if z.real < 0.5:
return pi / (sin(pi*z)*gamma(1-z))
else:
z -= 1
x = p
for i in range(1, g+2):
x += p[i]/(z+i)
t = z + g + 0.5
return sqrt(2*pi) * t**(z+0.5) * exp(-t) * x

This works in Python 3.0

But I can't figure out where it gets "cmath".    Searching the Python
directory reveals no more than a test_cmath.  The only cmath I can find
is a header file in another directory  turboc++\Borland\include\

dir(cmath) reveals 23 functions overlapping the 37 functions of
the math module.

What is cmath, where did it come from and how does it differ from
the standard math module  ?

Dave WB3DWE
I saw the number 4 in silver,  Guido
(apologies to Wm Carlos Williams)

```