add new graphs

3 files changed, 56 insertions, 0 deletions

diff --git a/buch/chapters/040-rekursion/gammalimit/Makefile b/buch/chapters/040-rekursion/gammalimit/Makefile
new file mode 100644
index 0000000..0804e74
--- /dev/null
+++ b/buch/chapters/040-rekursion/gammalimit/Makefile
@@ -0,0 +1,11 @@
+#
+# Makefile -- build gamma limit test programm
+#
+# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+#
+l:	l.cpp
+	g++ -O2 -g -Wall `pkg-config --cflags gsl` `pkg-config --libs gsl` \
+		-o l l.cpp
+
+test:	l
+	./l
diff --git a/buch/chapters/040-rekursion/gammalimit/l.cpp b/buch/chapters/040-rekursion/gammalimit/l.cpp
new file mode 100644
index 0000000..7a86800
--- /dev/null
+++ b/buch/chapters/040-rekursion/gammalimit/l.cpp
@@ -0,0 +1,26 @@
+/*
+ * l.cpp
+ *
+ * (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+ */
+#include <cstdlib>
+#include <cmath>
+#include <cstdio>
+
+int	main(int argc, char *argv[]) {
+	double	x = 0.5;
+	double	g = tgamma(x);
+	printf("limit: %20.16f\n", g);
+	double	p = 1;
+	long long	N = 100000000000;
+	long long	n = 10;
+	for (long long k = 1; k <= N; k++) {
+		p = p * k / (x + k - 1);
+		if (0 == k % n) {
+			double	gval = p * pow(k, x-1);
+			printf("%12ld  %20.16f %20.16f\n", k, gval, gval - g);
+			n = n * 10;
+		}
+	}
+	return EXIT_SUCCESS;
+}
diff --git a/buch/chapters/040-rekursion/gammalimit/l.m b/buch/chapters/040-rekursion/gammalimit/l.m
new file mode 100644
index 0000000..32b6442
--- /dev/null
+++ b/buch/chapters/040-rekursion/gammalimit/l.m
@@ -0,0 +1,19 @@
+#
+# l.m -- Berechnung der Gamma-Funktion
+#
+# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+#
+global N;
+N = 10000;
+
+function retval = gamma(x, n)
+	p = 1;
+	for k = (1:n)
+		p = p * k / (x + k - 1);
+	end
+	retval = p * n^(x-1);
+endfunction
+
+for n = (100:100:N)
+	printf("Gamma(%4d) = %10f\n", n, gamma(0.5, n));
+end