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;;;; 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)))
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