From b5d63d656dd32a537197b2164d10a8f56cbfc1ac Mon Sep 17 00:00:00 2001
From: Mohammad S Anwar <mohammad.anwar@yahoo.com>
Date: Wed, 1 Jun 2022 12:29:50 +0100
Subject: - Added guest contribution by Eric Cheung.

---
 challenge-167/eric-cheung/python/ch-2.py | 42 ++++++++++++++++++++++++++++++++
 1 file changed, 42 insertions(+)
 create mode 100755 challenge-167/eric-cheung/python/ch-2.py

(limited to 'challenge-167/eric-cheung/python/ch-2.py')

diff --git a/challenge-167/eric-cheung/python/ch-2.py b/challenge-167/eric-cheung/python/ch-2.py
new file mode 100755
index 0000000000..f6f799c698
--- /dev/null
+++ b/challenge-167/eric-cheung/python/ch-2.py
@@ -0,0 +1,42 @@
+
+## Remarks & Credit
+## https://en.wikipedia.org/wiki/Lanczos_approximation
+
+from cmath import sin, sqrt, pi, exp
+
+p = [676.5203681218851, -1259.1392167224028, 771.32342877765313, -176.61502916214059, 12.507343278686905, -0.13857109526572012, 9.9843695780195716e-6,1.5056327351493116e-7]
+
+EPSILON = 1e-07
+
+def drop_imag(z):
+    if abs(z.imag) <= EPSILON:
+        z = z.real
+
+    return z
+
+def gamma(z):
+    z = complex(z)
+
+    if z.real < 0.5:
+        y = pi / (sin(pi * z) * gamma(1 - z)) ## Reflection formula
+    else:
+        z = z - 1
+        x = 0.99999999999980993
+
+        for (i, pval) in enumerate(p):
+            x = x + pval / (z + i + 1)
+
+        t = z + len(p) - 0.5
+        y = sqrt(2 * pi) * t ** (z + 0.5) * exp(-t) * x
+
+    return drop_imag(y)
+
+"""
+The above use of the reflection (thus the if-else structure) is necessary, even though 
+it may look strange, as it allows to extend the approximation to values of z where 
+Re(z) < 0.5, where the Lanczos method is not valid.
+"""
+
+print(gamma(3))
+print(gamma(5))   
+print(gamma(7))
-- 
cgit