From 1a65f1e2cc20e1dfe5d0d88cf42ee7355c20b1ff Mon Sep 17 00:00:00 2001
From: Fabian <@>
Date: Sat, 13 Aug 2022 22:27:32 +0200
Subject: 2. Ueberarbeitung

---
 buch/papers/0f1/listings/kettenbruchIterativ.c | 60 ++++++++------------------
 1 file changed, 17 insertions(+), 43 deletions(-)

(limited to 'buch/papers/0f1/listings/kettenbruchIterativ.c')

diff --git a/buch/papers/0f1/listings/kettenbruchIterativ.c b/buch/papers/0f1/listings/kettenbruchIterativ.c
index d897b8f..3caaf43 100644
--- a/buch/papers/0f1/listings/kettenbruchIterativ.c
+++ b/buch/papers/0f1/listings/kettenbruchIterativ.c
@@ -1,53 +1,27 @@
 /**
-  * @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)
+  * @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)
   * @return Result
   */
-static double fractionRekursion0f1(const double c, const double z, unsigned int n)
+static double fractionIter0f1(const double c, const double z, unsigned int k)
 {
     //declaration
     double a = 0.0;
     double b = 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;
+    double abk = 0.0;
+    double temp = 0.0;
 
-    for (unsigned int k = 0; k <= n; ++k)
+    for (; k > 0; --k)
     {
-        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; 
+        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)
     }
-    //approximation fraction
-    return  Ak/Bk;
-}
+
+    return a + temp;                    //a0 + temp
+}
\ No newline at end of file
-- 
cgit v1.2.1