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Sums of digits and the Hurwitz zeta function

1990
Let s2(n) denote the sum of the binary digits of n. Then it is easily seen that $$\sum\limits_{n = 1}^{ + \infty } {\frac{{s_2 (n)}}{{n(n + 1)}} = 2Log2.}$$
Jeffrey Shallit, Jean-Paul Allouche
openaire   +2 more sources

Monotonicity Properties of the Hurwitz Zeta Function

Canadian Mathematical Bulletin, 2005
AbstractLetbe the Hurwitz zeta function and letwhereα, β> 1 anda,b> 0 are real numbers. We prove: (i) The functionQis decreasing on (0, ∞) iffαa−βb≥ max(a−b, 0). (ii)Qis increasing on (0, ∞) iffαa−βb≤ min(a−b, 0). An application of part (i) reveals that for allx> 0 the functions⟼ [(s− 1)ζ(s,x)]1/(s−1)is decreasing on (1, ∞).
openaire   +2 more sources

Female erectile tissues and sexual dysfunction after pelvic radiotherapy: A scoping review

Ca-A Cancer Journal for Clinicians, 2022
Deborah C Marshall   +2 more
exaly  

Universality of the Hurwitz zeta-function in short intervals

Boletín de la Sociedad Matematica Mexicana
Antanas Laurinčikas
semanticscholar   +1 more source

On a Hilbert-Type Integral Inequality Related to the Extended Hurwitz Zeta Function in the Whole Plane

Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications, 2018
M. Rassias, Bicheng Yang
semanticscholar   +1 more source

A systematic review of rehabilitation and exercise recommendations in oncology guidelines

Ca-A Cancer Journal for Clinicians, 2021
Kathleen Doyle Lyons   +2 more
exaly  

The broadening scope of oral mucositis and oral ulcerative mucosal toxicities of anticancer therapies

Ca-A Cancer Journal for Clinicians, 2022
Michal Kuten-shorrer   +2 more
exaly  

Cancer epigenetics in clinical practice

Ca-A Cancer Journal for Clinicians, 2023
Veronica Davalos, Manel Esteller
exaly  

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