package org.nevec.rjm;

/**
 * Harmonic numbers.
 * H(n) is the sum of the inverses of the integers from 1 to n.
 *
 * @since 2008-10-19
 * @author Richard J. Mathar
 */
public class Harmonic {
	/**
	 * ctor()
	 * Does nothing.
	 */
	public Harmonic() {}

	/**
	 * The Harmonic number at the index specified
	 *
	 * @param n
	 *            the index, non-negative.
	 * @return the H_1=1 for n=1, H_2=3/2 for n=2 etc.
	 *         For values of n less than 1, zero is returned.
	 */
	public Rational at(final int n) {
		if (n < 1) {
			return new Rational(0, 1);
		} else {
			/*
			 * start with 1 as the result
			 */
			Rational a = new Rational(1, 1);

			/*
			 * add 1/i for i=2..n
			 */
			for (int i = 2; i <= n; i++) {
				a = a.add(new Rational(1, i));
			}
			return a;
		}
	}
} /* Harmonic */