From f3ced170faef47bcdf76f96eabf0534a58fd348e Mon Sep 17 00:00:00 2001
From: Fabian <@>
Date: Fri, 22 Jul 2022 16:31:41 +0200
Subject: 0f1, struktur
---
buch/papers/0f1/images/airy.pdf | Bin 0 -> 25568 bytes
buch/papers/0f1/images/konvergenzAiry.pdf | Bin 0 -> 15137 bytes
buch/papers/0f1/images/konvergenzNegativ.pdf | Bin 0 -> 16312 bytes
buch/papers/0f1/images/konvergenzPositiv.pdf | Bin 0 -> 18924 bytes
buch/papers/0f1/images/stabilitaet.pdf | Bin 0 -> 20944 bytes
buch/papers/0f1/listings/kettenbruchIterativ.c | 45 ++++++++++++++++++++++++
buch/papers/0f1/listings/kettenbruchRekursion.c | 19 ++++++++++
buch/papers/0f1/listings/potenzreihe.c | 13 +++++++
8 files changed, 77 insertions(+)
create mode 100644 buch/papers/0f1/images/airy.pdf
create mode 100644 buch/papers/0f1/images/konvergenzAiry.pdf
create mode 100644 buch/papers/0f1/images/konvergenzNegativ.pdf
create mode 100644 buch/papers/0f1/images/konvergenzPositiv.pdf
create mode 100644 buch/papers/0f1/images/stabilitaet.pdf
create mode 100644 buch/papers/0f1/listings/kettenbruchIterativ.c
create mode 100644 buch/papers/0f1/listings/kettenbruchRekursion.c
create mode 100644 buch/papers/0f1/listings/potenzreihe.c
(limited to 'buch/papers/0f1')
diff --git a/buch/papers/0f1/images/airy.pdf b/buch/papers/0f1/images/airy.pdf
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diff --git a/buch/papers/0f1/images/konvergenzAiry.pdf b/buch/papers/0f1/images/konvergenzAiry.pdf
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index 0000000..2e635ea
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diff --git a/buch/papers/0f1/images/konvergenzNegativ.pdf b/buch/papers/0f1/images/konvergenzNegativ.pdf
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index 0000000..3b58be4
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diff --git a/buch/papers/0f1/images/konvergenzPositiv.pdf b/buch/papers/0f1/images/konvergenzPositiv.pdf
new file mode 100644
index 0000000..24e3fd5
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diff --git a/buch/papers/0f1/images/stabilitaet.pdf b/buch/papers/0f1/images/stabilitaet.pdf
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index 0000000..be4af42
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diff --git a/buch/papers/0f1/listings/kettenbruchIterativ.c b/buch/papers/0f1/listings/kettenbruchIterativ.c
new file mode 100644
index 0000000..befea8e
--- /dev/null
+++ b/buch/papers/0f1/listings/kettenbruchIterativ.c
@@ -0,0 +1,45 @@
+static double fractionRekursion0f1(const double c, const double x, unsigned int n)
+{
+ 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;
+
+ for (unsigned int k = 0; k <= n; ++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 = x/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
+ //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;
+ }
+ //approximation fraction
+ return Ak/Bk;
+}
diff --git a/buch/papers/0f1/listings/kettenbruchRekursion.c b/buch/papers/0f1/listings/kettenbruchRekursion.c
new file mode 100644
index 0000000..958d4e1
--- /dev/null
+++ b/buch/papers/0f1/listings/kettenbruchRekursion.c
@@ -0,0 +1,19 @@
+static double fractionIter0f1(const double b0, const double z, unsigned int n)
+{
+ double a = 0.0;
+ double b = 0.0;
+ double abn = 0.0;
+ double temp = 0.0;
+
+ for (; n > 0; --n)
+ {
+ abn = z / (n * ((n - 1) + b0)); //abn = ak, bk
+
+ a = n > 1 ? (1 + abn) : 1; //a0, a1
+ b = n > 1 ? -abn : abn; //b1
+
+ temp = b / (a + 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
new file mode 100644
index 0000000..bfaa0e3
--- /dev/null
+++ b/buch/papers/0f1/listings/potenzreihe.c
@@ -0,0 +1,13 @@
+#include <math.h>
+
+static double powerseries(const double b, 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));
+ }
+
+ return temp;
+}
\ No newline at end of file
--
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