September 2017 Update

Task/Gamma-function/Phix/gamma-function.phix

@@ -0,0 +1,39 @@
+sequence c = repeat(0,12)
+
+function gamma(atom z)
+    atom accm = c[1]
+    if accm=0 then
+        accm = sqrt(2*PI)
+        c[1] = accm
+        atom k1_factrl = 1  -- (k - 1)!*(-1)^k with 0!==1
+        for k=2 to 12 do
+            c[k] = exp(13-k)*power(13-k,k-1.5)/k1_factrl
+            k1_factrl *= -(k-1)
+        end for
+    end if
+    for k=2 to 12 do
+        accm += c[k]/(z+k-1)
+    end for
+    accm *= exp(-(z+12))*power(z+12,z+0.5) -- Gamma(z+1)
+    return accm/z
+end function
+
+procedure sq(atom x, atom mul)
+atom p = x*mul
+    printf(1,"%18.16g,%18.15g\n",{x,p*p})
+end procedure
+
+procedure si(atom x)
+    printf(1,"%18.15f\n",{x})
+end procedure
+
+sq(gamma(-3/2),3/4)
+sq(gamma(-1/2),-1/2)
+sq(gamma(1/2),1)
+si(gamma(1))
+sq(gamma(3/2),2)
+si(gamma(2))
+sq(gamma(5/2),4/3)
+si(gamma(3))
+sq(gamma(7/2),8/15)
+si(gamma(4))