247 citations
- Tunis El Manar UniversityTN26 papers
- Tunis UniversityTN20 papers
- Centre National de la Recherche ScientifiqueFR5 papers
- Laboratoire d'Automatique, Génie Informatique et SignalFR5 papers
- National Institute of Applied Science and TechnologyTN4 papers
- École Centrale de LilleFR3 papers
- Université de ToulonFR3 papers
- University of MonastirTN3 papers
- Aix-Marseille UniversitéFR2 papers
- École Nationale d'Ingénieurs de TarbesFR2 papers
- École Normale Supérieure - PSLFR2 papers
- ENSITTN2 papers
6 papers · 1 filter
The Riemann Hypothesis: A Qualitative Characterization of the Nontrivial Zeros of the Riemann Zeta Function Using Polylogarithms
Lazhar Fekih-Ahmed
We formulate a parametrized uniformly absolutely globally convergent series of (s) denoted by Z(s, x). When expressed in closed form, it is given by Z(s, x) = (s -- 1)(s) + 1…
On the Power Series Expansion of the Reciprocal Gamma Function
Lazhar Fekih-Ahmed
Using the reflection formula of the Gamma function, we derive a new formula for the Taylor coefficients of the reciprocal Gamma function. The new formula provides effective asympto…
A New Effective Asymptotic Formula for the Stieltjes Constants
Lazhar Fekih-Ahmed
We derive a new integral formula for the Stieltjes constants. The new formula permits easy computations as well as an exact approximate asymptotic formula. Both the sign oscillatio…
A Necessary Condition for a Nontrivial Zero of the Riemann Zeta Function via the Polylogarithmic Function
Lazhar Fekih-Ahmed
The author has found today an error in the denominator of the residue equation (4.5). This unfortunate mistake makes the conclusions and the title of the paper incorrect. The funct…
On Some Explicit Formulas for Bernoulli Numbers and Polynomials
Lazhar Fekih-Ahmed
We provide direct elementary proofs of several explicit expressions for Bernoulli numbers and Bernoulli polynomials. As a byproduct of our method of proof, we provide natural defin…
On the Hurwitz Zeta Function
Lazhar Fekih-Ahmed
We give new integral and series representations of the Hurwitz zeta function. We also provide a closed-form expression of the coefficients of the Laurent expansion of the Hurwitz-z…