1 files changed, 24 insertions, 0 deletions
diff --git a/guile/net/ricketyspace/taocp/one/two/seven/hn.scm b/guile/net/ricketyspace/taocp/one/two/seven/hn.scm
new file mode 100644
index 0000000..68d16dc
--- /dev/null
+++ b/guile/net/ricketyspace/taocp/one/two/seven/hn.scm
@@ -0,0 +1,24 @@
+;;;; copyright 2016 rsiddharth <s@ricketyspace.net>
+;;;; under gnu general public license version 3 or higher.
+
+(define-module (net ricketyspace taocp one two seven hn)
+  #:export (compute-hn
+            compute-h2^m
+            h2^m-relation))
+
+;;; compute H_n
+(define (compute-hn n)
+  (cond ((= 1 n) 1.0)
+        (else (+ (/ 1.0 n) (compute-hn (1- n))))))
+
+;;; compute H_2^m
+(define (compute-h2^m m)
+  (let* ((n (expt 2 m)))
+    (compute-hn n)))
+
+;;; H_2^m >= 1 + m/2 relation
+(define (h2^m-relation m)
+  (let ((2^m (expt 2 m))
+        (h2^m (compute-h2^m m))
+        (rhs (+ 1.0 (/ m 2.0))))
+    (list 2^m h2^m rhs)))