diff options
author | haddoucher <reda.haddouche@ost.ch> | 2022-08-16 14:36:07 +0200 |
---|---|---|
committer | haddoucher <reda.haddouche@ost.ch> | 2022-08-16 14:36:07 +0200 |
commit | f031b148a79d1dafb0e3405643be05e7a7eb1222 (patch) | |
tree | 3f0c7d27ba90e10874a885cae9026fdbaa0b01e6 /buch/papers/0f1/listings | |
parent | Update tschebyscheff_beispiel.tex (diff) | |
parent | Merge pull request #5 from haddoucher/sturmliouville/erik-branch (diff) | |
download | SeminarSpezielleFunktionen-f031b148a79d1dafb0e3405643be05e7a7eb1222.tar.gz SeminarSpezielleFunktionen-f031b148a79d1dafb0e3405643be05e7a7eb1222.zip |
Merge remote-tracking branch 'origin/master' into sturmliouville/redabranch
Diffstat (limited to '')
-rw-r--r-- | buch/papers/0f1/listings/kettenbruchIterativ.c | 16 | ||||
-rw-r--r-- | buch/papers/0f1/listings/kettenbruchRekursion.c | 24 | ||||
-rw-r--r-- | buch/papers/0f1/listings/potenzreihe.c | 60 |
3 files changed, 86 insertions, 14 deletions
diff --git a/buch/papers/0f1/listings/kettenbruchIterativ.c b/buch/papers/0f1/listings/kettenbruchIterativ.c index befea8e..d897b8f 100644 --- a/buch/papers/0f1/listings/kettenbruchIterativ.c +++ b/buch/papers/0f1/listings/kettenbruchIterativ.c @@ -1,5 +1,13 @@ -static double fractionRekursion0f1(const double c, const double x, unsigned int n)
+/**
+ * @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 fractionRekursion0f1(const double c, const double z, unsigned int n)
{
+ //declaration
double a = 0.0;
double b = 0.0;
double Ak = 0.0;
@@ -21,15 +29,15 @@ static double fractionRekursion0f1(const double c, const double x, unsigned int else if (k == 1)
{
a = 1.0; //a1
- b = x/c; //b1
+ b = z/c; //b1
//recursion fomula for A1, B1
Ak = a * Ak_1 + b * 1.0;
Bk = a * Bk_1;
}
else
{
- a = 1 + (x / (k * ((k - 1) + c)));//ak
- b = -(x / (k * ((k - 1) + c))); //bk
+ 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;
diff --git a/buch/papers/0f1/listings/kettenbruchRekursion.c b/buch/papers/0f1/listings/kettenbruchRekursion.c index 958d4e1..3caaf43 100644 --- a/buch/papers/0f1/listings/kettenbruchRekursion.c +++ b/buch/papers/0f1/listings/kettenbruchRekursion.c @@ -1,19 +1,27 @@ -static double fractionIter0f1(const double b0, const double z, unsigned int n)
+/**
+ * @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 fractionIter0f1(const double c, const double z, unsigned int k)
{
+ //declaration
double a = 0.0;
double b = 0.0;
- double abn = 0.0;
+ double abk = 0.0;
double temp = 0.0;
- for (; n > 0; --n)
+ for (; k > 0; --k)
{
- abn = z / (n * ((n - 1) + b0)); //abn = ak, bk
+ abk = z / (k * ((k - 1) + c)); //abk = ak, bk
- a = n > 1 ? (1 + abn) : 1; //a0, a1
- b = n > 1 ? -abn : abn; //b1
+ a = k > 1 ? (1 + abk) : 1; //a0, a1
+ b = k > 1 ? -abk : abk; //b1
- temp = b / (a + temp);
+ temp = b / (a + temp); //bk / (ak + last result)
}
- return a + temp; //a0 + temp
+ return a + temp; //a0 + temp
}
\ No newline at end of file diff --git a/buch/papers/0f1/listings/potenzreihe.c b/buch/papers/0f1/listings/potenzreihe.c index bfaa0e3..23fdfea 100644 --- a/buch/papers/0f1/listings/potenzreihe.c +++ b/buch/papers/0f1/listings/potenzreihe.c @@ -1,12 +1,68 @@ #include <math.h>
-static double powerseries(const double b, const double z, unsigned int n)
+/**
+ * @brief Calculates pochhammer
+ * @param (a+n-1)!
+ * @return Result
+ */
+static double pochhammer(const double x, double n)
+{
+ double temp = x;
+
+ if (n > 0)
+ {
+ while (n > 1)
+ {
+ temp *= (x + n - 1);
+ --n;
+ }
+
+ return temp;
+ }
+ else
+ {
+ return 1;
+ }
+}
+
+/**
+ * @brief Calculates the Factorial
+ * @param n!
+ * @return Result
+ */
+static double fac(int n)
+{
+ double temp = n;
+
+ if (n > 0)
+ {
+ while (n > 1)
+ {
+ --n;
+ temp *= n;
+ }
+ return temp;
+ }
+ else
+ {
+ return 1;
+ }
+}
+
+/**
+ * @brief Calculates the Hypergeometric Function 0F1(;b;z)
+ * @param c in 0F1(;c;z)
+ * @param z in 0F1(;c;z)
+ * @param n number of itertions (precision)
+ * @return Result
+ */
+static double powerseries(const double c, const double z, unsigned int n)
{
double temp = 0.0;
for (unsigned int k = 0; k < n; ++k)
{
- temp += pow(z, k) / (factorial(k) * pochhammer(b, k));
+ temp += pow(z, k) / (factorial(k) * pochhammer(c, k));
}
return temp;
|