harmonic.cpp File Reference

#include "divisors.hpp"
#include "harmonic.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...
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...

Variables
const double	sigmaodd::alpha = 0.425
const double	sigmaodd::alpha_bis = 0.7
const double	sigmaodd::beta = 0.40580406331047491619301581522449851
const double	sigmaodd::euler_gamma = 0.577215664901532860606512090082402431042
	The Euler-Mascheroni constant 0.577215664901532860606512090082402431042... (rounded to an upper bound in double) http://mathworld.wolfram.com/Euler-MascheroniConstant.html. More...

Detailed Description

(February 14, 2018)

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

Definition in file harmonic.cpp.