harmonic.hpp File Reference

Function to calculate harmonic number H_n = 1 + 1/2 + 1/3 + 1/4 + ... + 1/n and some variants and upper bounds. More...

#include "helper.hpp"
#include "harmonic__inline.hpp"

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Namespaces
	sigmaodd
	A lot of functions and stuffs to deal the sigma_odd problem and related stuffs.

Functions
double	sigmaodd::diff_half_harmonic_upper_bound (nat_type a, nat_type b)
	Return an upper bound of H_a - 1/2 H_b. More...
double	sigmaodd::diff_half_harmonic_upper_bound (nat_type n)
	Return an upper bound of H_n - 1/2 H_k with k = floor(n/2). More...
double	sigmaodd::diff_harmonic_upper_bound (nat_type a, nat_type b)
	Return an upper bound of H_a - H_b. More...
constexpr double	sigmaodd::harmonic (nat_type n)
	Return the harmonic number H_n = 1/1 + 1/2 + 1/3 + 1/4 + ... + 1/n. More...
constexpr double	sigmaodd::harmonic_even (nat_type n)
	Return 1/2 + 1/4 + 1/6 + 1/8 + ... + (1/n or 1/(n-1)). More...
constexpr double	sigmaodd::harmonic_odd (nat_type n)
	Return 1/1 + 1/3 + 1/5 + 1/7 + ... + (1/n or 1/(n-1)). More...
double	sigmaodd::harmonic_lower_bound (nat_type n)
	Return a lower bound of H_n. More...
double	sigmaodd::harmonic_upper_bound (nat_type n)
	Return an upper bound of H_n. More...
nat_type	sigmaodd::sum_floor_n_harmonic_odd (nat_type n, nat_type to_n)
	Return floor(n/1) + floor(n/3) + floor(n/5) + floor(n/7) + ... + (n/to_n or floor(1/(to_n-1))). More...

Detailed Description

Function to calculate harmonic number H_n = 1 + 1/2 + 1/3 + 1/4 + ... + 1/n and some variants and upper bounds.

(February 14, 2018) http://mathworld.wolfram.com/HarmonicNumber.html

GPLv3 — Copyright (C) 2017, 2018 Olivier Pirson http://www.opimedia.be/

Definition in file harmonic.hpp.