1 files changed, 43 insertions, 17 deletions
diff --git a/buch/papers/0f1/listings/kettenbruchRekursion.c b/buch/papers/0f1/listings/kettenbruchRekursion.c
index 3caaf43..d897b8f 100644
--- a/buch/papers/0f1/listings/kettenbruchRekursion.c
+++ b/buch/papers/0f1/listings/kettenbruchRekursion.c
@@ -1,27 +1,53 @@
 /**
-  * @brief Calculates the Hypergeometric Function 0F1(;c;z)
-  * @param c in 0F1(;c;z)
-  * @param z in 0F1(;c;z)
-  * @param k number of itertions (precision)
+  * @brief Calculates the Hypergeometric Function 0F1(;b;z)
+  * @param b0 in 0F1(;b0;z)
+  * @param z in 0F1(;b0;z)
+  * @param n number of itertions (precision)
   * @return Result
   */
-static double fractionIter0f1(const double c, const double z, unsigned int k)
+static double fractionRekursion0f1(const double c, const double z, unsigned int n)
 {
     //declaration
     double a = 0.0;
     double b = 0.0;
-    double abk = 0.0;
-    double temp = 0.0;
+    double Ak = 0.0;
+    double Bk = 0.0;
+    double Ak_1 = 0.0;
+    double Bk_1 = 0.0;
+    double Ak_2 = 0.0;
+    double Bk_2 = 0.0;
 
-    for (; k > 0; --k)
+    for (unsigned int k = 0; k <= n; ++k)
     {
-        abk = z / (k * ((k - 1) + c));  //abk = ak, bk
-        
-        a = k > 1 ? (1 + abk) : 1;      //a0, a1
-        b = k > 1 ? -abk : abk;         //b1
-
-        temp = b / (a + temp);          //bk / (ak + last result)
+        if (k == 0)
+        {
+            a = 1.0; //a0
+            //recursion fomula for A0, B0
+            Ak = a;
+            Bk = 1.0;
+        }
+        else if (k == 1)
+        {
+            a = 1.0; //a1
+            b = z/c; //b1
+            //recursion fomula for A1, B1
+            Ak = a * Ak_1 + b * 1.0;
+            Bk = a * Bk_1;
+        }
+        else
+        {
+            a = 1 + (z / (k * ((k - 1) + c)));//ak
+            b = -(z / (k * ((k - 1) + c)));   //bk
+            //recursion fomula for Ak, Bk
+            Ak = a * Ak_1 + b * Ak_2;
+            Bk = a * Bk_1 + b * Bk_2;
+        }        
+        //save old values
+        Ak_2 = Ak_1;
+        Bk_2 = Bk_1;
+        Ak_1 = Ak;
+        Bk_1 = Bk; 
     }
-
-    return a + temp;                    //a0 + temp
-}
-\ No newline at end of file
+    //approximation fraction
+    return  Ak/Bk;
+}