Initial data commit

Task/Gamma-function/F-Sharp/gamma-function-1.fs

@@ -0,0 +1,14 @@
+open System
+
+let gamma z =
+    let lanczosCoefficients = [76.18009172947146;-86.50532032941677;24.01409824083091;-1.231739572450155;0.1208650973866179e-2;-0.5395239384953e-5]
+    let rec sumCoefficients acc i coefficients =
+        match coefficients with
+        | []   -> acc
+        | h::t -> sumCoefficients (acc + (h/i)) (i+1.0) t
+    let gamma = 5.0
+    let x = z - 1.0
+    Math.Pow(x + gamma + 0.5, x + 0.5) * Math.Exp( -(x + gamma + 0.5) ) * Math.Sqrt( 2.0 * Math.PI ) * sumCoefficients 1.000000000190015 (x + 1.0) lanczosCoefficients
+
+seq { for i in 1 .. 20 do yield ((double)i/10.0) } |> Seq.iter ( fun v -> System.Console.WriteLine("{0} : {1}", v, gamma v ) )
+seq { for i in 1 .. 10 do yield ((double)i*10.0) } |> Seq.iter ( fun v -> System.Console.WriteLine("{0} : {1}", v, gamma v ) )

Task/Gamma-function/F-Sharp/gamma-function-2.fs

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+open System.Numerics
+open System
+
+let rec gamma (z: Complex) =
+    let mutable z = z
+    let lanczosCoefficients = [| 676.520368121885; -1259.1392167224; 771.323428777653; -176.615029162141; 12.5073432786869; -0.13857109526572; 9.98436957801957E-06; 1.50563273514931E-07 |]
+
+    if z.Real < 0.5 then
+        Math.PI / (sin (Math.PI * z) * gamma (1.0 - z))
+    else
+        let mutable x = Complex.One
+        z <- z - 1.0
+
+        for i = 0 to lanczosCoefficients.Length - 1 do
+            x <- x + lanczosCoefficients.[i] / (z + Complex(i, 0) + 1.0)
+
+        let t = z + float lanczosCoefficients.Length - 0.5
+        sqrt (2.0 * Math.PI) * (t ** (z + 0.5)) * exp (-t) * x
+
+Seq.iter (fun i -> printfn "Gamma(%f) = %A" i (gamma (Complex(i, 0)))) [ 0 .. 100 ]
+Seq.iter2 (fun i j -> printfn "Gamma(%f + i%f) = %A" i j (gamma (Complex(i, j)))) [ 0 .. 100 ] [ 0 .. 100 ]