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Factorial: Difference between revisions
→[[Factorial function#Python]]
(Python: Functional with sample output) |
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:</python>
===Numerical Approximation===
The following sample uses Lanczos approximation from http://en.wikipedia.org/wiki/Lanczos_approximation
<python>
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[0]
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
def factorial(n):
return gamma(n+1)
print "factorial(-0.5)**2=",factorial(-0.5)**2
for i in range(10):
print "factorial(%d)=%s"%(i,factorial(i))
</python>
Output:
<pre>
factorial(-0.5)**2= (3.14159265359+0j)
factorial(0)=(1+0j)
factorial(1)=(1+0j)
factorial(2)=(2+0j)
factorial(3)=(6+0j)
factorial(4)=(24+0j)
factorial(5)=(120+0j)
factorial(6)=(720+0j)
factorial(7)=(5040+0j)
factorial(8)=(40320+0j)
factorial(9)=(362880+0j)
</pre>
===Recursive===
<python>def factorial(n):
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